Cristian Lenart

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All published works

Action	Title	Year	Authors
+	A general Chevalley formula for semi-infinite flag manifolds and quantum K-theory	2024	Cristian Lenart Satoshi Naito Daisuke Sagaki
+	Quantum K-theory Chevalley formulas in the parabolic case	2024	Takafumi Kouno Cristian Lenart Satoshi Naito Daisuke Sagaki Weihong Xu
+ PDF Chat	New structure on the quantum alcove model with applications to representation theory and Schubert calculus	2023	Takafumi Kouno Cristian Lenart Satoshi Naito
+ PDF Chat	Inverse K-Chevalley formulas for semi-infinite flag manifolds, II: Arbitrary weights in ADE type	2023	Cristian Lenart Satoshi Naito Daniel L. Orr Daisuke Sagaki
+ PDF Chat	Geometric properties of the Kazhdan–Lusztig Schubert basis	2023	Cristian Lenart Changjian Su Kirill Zainoulline Changlong Zhong
+ PDF Chat	Geometric properties of the Kazhdan–Lusztig Schubert basis	2023	Cristian Lenart Changjian Su Kirill Zainoulline Changlong Zhong
+	Elliptic classes via the periodic Hecke module and its Langlands dual	2023	Cristian Lenart Gufang Zhao Changlong Zhong
+	Symmetric and Nonsymmetric Macdonald Polynomials via a Path Model with a Pseudo-crystal Structure	2022	Cristian Lenart Satoshi Naito Fumihiko Nomoto Daisuke Sagaki
+	Towards a Combinatorial Model for $q$-weight Multiplicities of Simple Lie Algebras (Extended Abstract)	2021	Cédric Lecouvey Cristian Lenart Adam Schultze
+	Generalization of quantum Yang-Baxter moves	2021	Takafumi Kouno Cristian Lenart Satoshi Naito
+	On Combinatorial Models for Affine Crystals	2021	Carly J. A. Briggs Cristian Lenart Adam Schultze
+	Relating three combinatorial formulas for type $A$ Whittaker functions	2021	Cristian Lenart James Sidoli
+	Inverse $K$-Chevalley formulas for semi-infinite flag manifolds, II: arbitrary weights in ADE type	2021	Cristian Lenart Satoshi Naito Daniel L. Orr Daisuke Sagaki
+	Towards a Combinatorial Model for $q$-weight Multiplicities of Simple Lie Algebras (Extended Abstract)	2021	Cédric Lecouvey Cristian Lenart Adam Schultze
+	Quantum K-theory Chevalley formulas in the parabolic case	2021	Takafumi Kouno Cristian Lenart Satoshi Naito Daisuke Sagaki
+	Lusztig’s t-Analogue of Weight Multiplicity via Crystals	2020	Cédric Lecouvey Cristian Lenart
+ PDF Chat	Atomic decomposition of characters and crystals	2020	Cédric Lecouvey Cristian Lenart
+	Geometric properties of the Kazhdan-Lusztig Schubert basis	2020	Cristian Lenart Changjian Su Kirill Zainoulline Changlong Zhong
+	A general Chevalley formula for semi-infinite flag manifolds and quantum K-theory	2020	Cristian Lenart Satoshi Naito Daisuke Sagaki
+	A Chevalley formula for semi-infinite flag manifolds and quantum K-theory (Extended abstract)	2019	Cristian Lenart Satoshi Naito Daisuke Sagaki
+	On higher level Kirillov–Reshetikhin crystals, Demazure crystals, and related uniform models	2019	Cristian Lenart Travis Scrimshaw
+ PDF Chat	PARABOLIC KAZHDAN–LUSZTIG BASIS, SCHUBERT CLASSES, AND EQUIVARIANT ORIENTED COHOMOLOGY	2019	Cristian Lenart Kirill Zainoulline Changlong Zhong
+	A Chevalley formula for semi-infinite flag manifolds and quantum K-theory (Extended abstract)	2019	Cristian Lenart Satoshi Naito Daisuke Sagaki
+ PDF Chat	Quantum Lakshmibai-Seshadri paths and root operators	2018	Cristian Lenart Satoshi Naito Daisuke Sagaki Anne Schilling Mark Shimozono
+ PDF Chat	A uniform realization of the combinatorial R-matrix for column shape Kirillov–Reshetikhin crystals	2018	Cristian Lenart Arthur Lubovsky
+ PDF Chat	Combinatorics of Generalized Exponents	2018	Cédric Lecouvey Cristian Lenart
+ PDF Chat	COMBINATORICS OF GENERALIZED EXPONENTS	2017	Cédric Lecouvey Cristian Lenart
+ PDF Chat	COMBINATORICS OF GENERALIZED EXPONENTS	2017	Cédric Lecouvey Cristian Lenart
+ PDF Chat	WHITTAKER FUNCTIONS AND DEMAZURE CHARACTERS	2017	Kyu‐Hwan Lee Cristian Lenart Dongwen Liu
+ PDF Chat	A UNIFORM MODEL FOR KIRILLOV–RESHETIKHIN CRYSTALS III: NONSYMMETRICMACDONALD POLYNOMIALS AT t = 0 AND DEMAZURE CHARACTERS	2017	Cristian Lenart Seiji Naito Daisuke Sagaki Anne Schilling Mark Shimozono
+	New results on Kirillov-Reshetikhin modules and Macdonald polynomials	2017	Cristian Lenart
+ PDF Chat	Towards generalized cohmology Schubert calculus via formal root polynomials	2017	Cristian Lenart Kirill Zainoulline
+	Combinatorics of generalized exponents	2017	Cédric Lecouvey Cristian Lenart
+ PDF Chat	Combinatorial representation theory of Lie algebras. Richard Stanley’s work and the way it was continued	2016	Cristian Lenart
+ PDF Chat	From the weak Bruhat order to crystal posets	2016	Patricia Hersh Cristian Lenart
+ PDF Chat	A Uniform Model for Kirillov–Reshetikhin Crystals II. Alcove Model, Path Model, and $P=X$	2016	Cristian Lenart Satoshi Naito Daisuke Sagaki Anne Schilling Mark Shimozono
+	Whittaker functions and Demazure characters	2016	Kyu‐Hwan Lee Cristian Lenart Dongwen Liu Dinakar Muthiah Anna Puskás
+	Parabolic Kazhdan-Lusztig basis, Schubert classes, and equivariant oriented cohomology	2016	Cristian Lenart Kirill Zainoulline Changlong Zhong
+	Whittaker functions and Demazure characters	2016	Kyu‐Hwan Lee Cristian Lenart Dongwen Liu Dinakar Muthiah Anna Puskás
+	From the weak Bruhat order to crystal posets	2015	Patricia Hersh Cristian Lenart
+	A Schubert basis in equivariant elliptic cohomology	2015	Cristian Lenart Kirill Zainoulline
+ PDF Chat	On Schubert calculus in elliptic cohomology	2015	Cristian Lenart Kirill Zainoulline
+	Explicit description of the degree function in terms of quantum Lakshmibai-Seshadri paths	2015	Cristian Lenart Satoshi Naito Daisuke Sagaki Anne Schilling Mark Shimozono
+	The many faces of modern combinatorics	2015	Cristian Lenart
+	Explicit description of the degree function in terms of quantum Lakshmibai-Seshadri paths	2015	Cristian Lenart Satoshi Naito Daisuke Sagaki Anne Schilling Mark Shimozono
+ PDF Chat	On Schubert calculus in elliptic cohomology	2015	Cristian Lenart Kirill Zainoulline
+ PDF Chat	A uniform realization of the combinatorial $R$-matrix	2015	Cristian Lenart Arthur Lubovsky
+	From the weak Bruhat order to crystal posets	2015	Patricia Hersh Cristian Lenart
+	The many faces of modern combinatorics	2015	Cristian Lenart
+	A Schubert basis in equivariant elliptic cohomology	2015	Cristian Lenart Kirill Zainoulline
+ PDF Chat	Equivariant K -Chevalley rules for Kac-Moody flag manifolds	2014	Cristian Lenart Mark Shimozono
+ PDF Chat	A generalization of the alcove model and its applications	2014	Cristian Lenart Arthur Lubovsky
+ PDF Chat	A Uniform Model for Kirillov-Reshetikhin Crystals I: Lifting the Parabolic Quantum Bruhat Graph	2014	Cristian Lenart Seiji Naito Daisuke Sagaki Anne Schilling Mark Shimozono
+	Combinatorial representation theory of Lie algebras. Richard Stanley's work and the way it was continued	2014	Cristian Lenart
+	Specialized Macdonald polynomials, quantum K-theory, and Kirillov-Reshetikhin crystals	2013	Cristian Lenart
+	Explicit description of the action of root operators on quantum Lakshmibai-Seshadri paths	2013	Cristian Lenart Satoshi Naito Daisuke Sagaki Anne Schilling Mark Shimozono
+ PDF Chat	A uniform model for Kirillov―Reshetikhin crystals	2013	Cristian Lenart Satoshi Naito Daisuke Sagaki Anne Schilling Mark Shimozono
+	Quantum Lakshmibai-Seshadri paths and root operators	2013	Cristian Lenart Satoshi Naito Daisuke Sagaki Anne Schilling Mark Shimozono
+ PDF Chat	Crystal energy functions via the charge in types A and C	2012	Cristian Lenart Anne Schilling
+	A uniform model for Kirillov-Reshetikhin crystals. Extended abstract	2012	Cristian Lenart Satoshi Naito Daisuke Sagaki Anne Schilling Mark Shimozono
+ PDF Chat	A generalization of the alcove model and its applications	2012	Cristian Lenart Arthur Lubovsky
+ PDF Chat	Crystal energy via charge	2012	Cristian Lenart Anne Schilling
+	Equivariant K-Chevalley Rules for Kac-Moody Flag Manifolds	2012	Cristian Lenart Mark Shimozono
+	A generalization of the alcove model and its applications	2011	Cristian Lenart Arthur Lubovsky
+ PDF Chat	From Macdonald polynomials to a charge statistic beyond type A	2011	Cristian Lenart
+	From Macdonald Polynomials to a Charge Statistic beyond Type A	2011	Cristian Lenart
+	A generalization of the alcove model and its applications	2011	Cristian Lenart Arthur Lubovsky
+	From Macdonald Polynomials to a Charge Statistic beyond Type A	2011	Cristian Lenart
+ PDF Chat	Haglund–Haiman–Loehr type formulas for Hall–Littlewood polynomials of type<i>B</i>and<i>C</i>	2010	Cristian Lenart
+	Hall–Littlewood polynomials, alcove walks, and fillings of Young diagrams	2010	Cristian Lenart
+ PDF Chat	Combinatorial Constructions of Weight Bases: The Gelfand-Tsetlin Basis	2010	Patricia Hersh Cristian Lenart
+ PDF Chat	Growth diagrams for the Schubert multiplication	2010	Cristian Lenart
+	Haglund-Haiman-Loehr Type Formulas for Hall-Littlewood Polynomials of Type B and C	2009	Cristian Lenart
+ PDF Chat	Combinatorial Formulas for Macdonald and Hall-Littlewood Polynomials	2009	Cristian Lenart
+	Growth Diagrams for the Schubert Multiplication	2009	Cristian Lenart
+ PDF Chat	On combinatorial formulas for Macdonald polynomials	2008	Cristian Lenart
+ PDF Chat	On q-analogs of weight multiplicities for the Lie superalgebras $\mathfrak{gl}(n,m)$ and $\mathfrak{spo(}2n,M)$	2008	Cédric Lecouvey Cristian Lenart
+	Hall-Littlewood Polynomials, Alcove Walks, and Fillings of Young Diagrams	2008	Cristian Lenart
+ PDF Chat	A combinatorial model for crystals of Kac-Moody algebras	2008	Cristian Lenart Alexander Postnikov
+	Combinatorial Formulas for Macdonald and Hall-Littlewood Polynomials of Types A and C. Extended Abstract	2008	Cristian Lenart
+	Combinatorial Constructions of Weight Bases: The Gelfand-Tsetlin Basis	2008	Patricia Hersh Cristian Lenart
+	On Combinatorial Formulas for Macdonald Polynomials	2008	Cristian Lenart
+	Hall-Littlewood Polynomials, Alcove Walks, and Fillings of Young Diagrams	2008	Cristian Lenart
+	On the combinatorics of crystal graphs, II. The crystal commutor	2007	Cristian Lenart
+ PDF Chat	Affine Weyl Groups in K-Theory and Representation Theory	2007	Cristian Lenart Alexander Postnikov
+	On q-analogs of weight multiplicities for the Lie superalgebras gl(n,m) and spo(2n,M)	2007	Cédric Lecouvey Cristian Lenart
+ PDF Chat	A Pieri-type formula for the ${K}$-theory of a flag manifold	2006	Cristian Lenart Frank Sottile
+ PDF Chat	On the combinatorics of crystal graphs, I. Lusztig's involution	2006	Cristian Lenart
+ PDF Chat	Grothendieck polynomials via permutation patterns and chains in the Bruhat order	2006	Cristian Lenart Shawn Robinson Frank Sottile
+	Quantum Grothendieck Polynomials	2006	Cristian Lenart Toshiaki Maeno
+ PDF Chat	Alcove path and Nichols-Woronowicz model of the equivariant K-theory of generalized flag varieties	2006	Cristian Lenart Toshiaki Maeno
+	Alcove path and Nichols-Woronowicz model of the equivariant $K$-theory of generalized flag varieties	2006	Cristian Lenart Toshiaki Maeno
+	On the Combinatorics of Crystal Graphs, II. The Crystal Commutator	2006	Cristian Lenart
+	On the Combinatorics of Crystal Graphs, I	2005	Cristian Lenart
+	On the Combinatorics of Crystal Graphs, I. Lusztig's Involution	2005	Cristian Lenart
+	A Combinatorial Model for Crystals of Kac-Moody Algebras	2005	Cristian Lenart Alexander Postnikov
+	The K-theory of the flag variety and the Fomin–Kirillov quadratic algebra	2004	Cristian Lenart
+ PDF Chat	A Unified Approach to Combinatorial Formulas for Schubert Polynomials	2004	Cristian Lenart
+	A Pieri-type formula for the K-theory of a flag manifold	2004	Cristian Lenart Frank Sottile
+	Grothendieck polynomials via permutation patterns and chains in the Bruhat order	2004	Cristian Lenart Shawn Robinson Frank Sottile
+	The K-theory of the Flag Variety and the Fomin-Kirillov Quadratic Algebra	2004	Cristian Lenart
+	A Unified Approach to Combinatorial Formulas for Schubert Polynomials	2004	Cristian Lenart
+	The K-theory of the Flag Variety and the Fomin-Kirillov Quadratic Algebra	2004	Cristian Lenart
+	A Pieri-type formula for the K-theory of a flag manifold	2004	Cristian Lenart Frank Sottile
+	Grothendieck polynomials via permutation patterns and chains in the Bruhat order	2004	Cristian Lenart Shawn Robinson Frank Sottile
+	Skew Schubert polynomials	2003	Cristian Lenart Frank Sottile
+	A K-theory version of Monk's formula and some related multiplication formulas	2003	Cristian Lenart
+	Affine Weyl groups in K-theory and representation theory	2003	Cristian Lenart Alexander Postnikov
+	Skew Schubert polynomials	2002	Cristian Lenart Frank Sottile
+	Skew Schubert polynomials	2002	Cristian Lenart Frank Sottile
+	Combinatorial Aspects of the K-Theory of Grassmannians	2000	Cristian Lenart
+ PDF Chat	None	2000	Cristian Lenart
+	Noncommutative Schubert Calculus and Grothendieck Polynomials	1999	Cristian Lenart
+	The Combinatorics of Steenrod Operations on the Cohomology of Grassmannians	1998	Cristian Lenart
+	Symmetric Functions, Formal Group Laws, and Lazard's Theorem	1998	Cristian Lenart
+	Hopf algebras of set systems	1998	Cristian Lenart Nigel Ray
+	Formal Group-Theoretic Generalizations of the Necklace Algebra, Including aq-Deformation	1998	Cristian Lenart
+	The combinatorics of Steenrod operations on the cohomology of Grassmannians	1997	Cristian Lenart
+	Chromatic polynomials of partition systems	1997	Cristian Lenart Nigel Ray
+	The combinatorics of Steenrod operations on the cohomology of Grassmannians	1997	Cristian Lenart

Common Coauthors

Coauthor	Papers Together
Satoshi Naito	19
Daisuke Sagaki	19
Mark Shimozono	12
Anne Schilling	12
Kirill Zainoulline	10
Cédric Lecouvey	10
Frank Sottile	9
Arthur Lubovsky	6
Changlong Zhong	6
Patricia Hersh	5
Takafumi Kouno	4
Alexander Postnikov	4
Dongwen Liu	3
Adam Schultze	3
Toshiaki Maeno	3
Kyu‐Hwan Lee	3
Changjian Su	3
Nigel Ray	2
Shawn Robinson	2
Daniel L. Orr	2
Dinakar Muthiah	2
Anna Puskás	2
Seiji Naito	2
Travis Scrimshaw	1
Weihong Xu	1
Carly J. A. Briggs	1
Shawn Robinson	1
Gufang Zhao	1
James Sidoli	1
Fumihiko Nomoto	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+ PDF Chat	A combinatorial model for crystals of Kac-Moody algebras	2008	Cristian Lenart Alexander Postnikov	37
+	Paths and Root Operators in Representation Theory	1995	Peter Littelmann	36
+ PDF Chat	Affine Weyl Groups in K-Theory and Representation Theory	2007	Cristian Lenart Alexander Postnikov	34
+	A Littlewood-Richardson rule for symmetrizable Kac-Moody algebras	1994	Peter Littelmann	34
+ PDF Chat	LS galleries, the path model, and MV cycles	2005	Stéphane Gaussent Peter Littelmann	26
+	None	1999	Francesco Brenti Sergey Fomin Alexander Postnikov	25
+	Crystal Graphs for Representations of the q-Analogue of Classical Lie Algebras	1994	Masaki Kashiwara Tohru Nakashima	22
+	A combinatorial formula for Macdonald polynomials	2010	Arun Ram Martha Yip	21
+ PDF Chat	A Uniform Model for Kirillov-Reshetikhin Crystals I: Lifting the Parabolic Quantum Bruhat Graph	2014	Cristian Lenart Seiji Naito Daisuke Sagaki Anne Schilling Mark Shimozono	20
+ PDF Chat	On the combinatorics of crystal graphs, I. Lusztig's involution	2006	Cristian Lenart	19
+ PDF Chat	From Macdonald polynomials to a charge statistic beyond type A	2011	Cristian Lenart	16
+	Reflection Groups and Coxeter Groups	1990	James E. Humphreys	16
+	Hecke algebras and shellings of Bruhat intervals	1993	Matthew Dyer	16
+ PDF Chat	A generalization of the alcove model and its applications	2014	Cristian Lenart Arthur Lubovsky	16
+	On crystal bases of the Q-analogue of universal enveloping algebras	1991	Masaki Kashiwara	15
+	A combinatorial formula for Macdonald polynomials	2005	J. Haglund Mark Haiman Nicholas A. Loehr	14
+ PDF Chat	On the quantum product of Schubert classes	2004	William Fulton Chris Woodward	14
+	REFLECTION GROUPS AND COXETER GROUPS (Cambridge Studies in Advanced Mathematics 29)	1991	R. W. Carter	14
+ PDF Chat	Demazure Crystals, Kirillov-Reshetikhin Crystals, and the Energy Function	2012	Anne Schilling Peter Tingley	14
+	Combinatorics of Coxeter Groups	2005	Anders Björner Francesco Brenti	14
+	Enumerative Combinatorics	1997	Richard P. Stanley Gian‐Carlo Rota	14
+ PDF Chat	A Uniform Model for Kirillov–Reshetikhin Crystals II. Alcove Model, Path Model, and $P=X$	2016	Cristian Lenart Satoshi Naito Daisuke Sagaki Anne Schilling Mark Shimozono	13
+	A symplectic jeu de taquin bijection between the tableaux of King and of De Concini	1999	John E. Sheats	13
+	Nonsymmetric Macdonald polynomials and Demazure characters	2003	Bogdan Ion	11
+ PDF Chat	Infinite-Dimensional Lie Algebras	1990	Victor G. Kač	11
+	A K-theory version of Monk's formula and some related multiplication formulas	2003	Cristian Lenart	11
+ PDF Chat	Lakshmibai–Seshadri paths of level-zero shape and one-dimensional sums associated to level-zero fundamental representations	2008	Satoshi Naito Daisuke Sagaki	11
+	A splitting criterion for the bruhat orderings on coxeter groups	1987	Vinay V. Deodhar	11
+	Standard monomial theory	1981	C. Musili C. S. Seshadri	11
+ PDF Chat	On combinatorial formulas for Macdonald polynomials	2008	Cristian Lenart	10
+	On level-zero representation of quantized affine algebras	2002	Masaki Kashiwara	10
+	Crystal structure on the set of Lakshmibai-Seshadri paths of an arbitrary level-zero shape	2007	Satoshi Naito Daisuke Sagaki	10
+	Crystalizing theq-analogue of universal enveloping algebras	1990	Masaki Kashiwara	10
+ PDF Chat	Alcove Walks, Hecke Algebras, Spherical Functions, Crystals and Column Strict Tableaux	2006	Arun Ram	10
+	Lusztig's q-analogue of weight multiplicity and one-dimensional sums for affine root systems	2006	Cédric Lecouvey Mark Shimozono	10
+	A Pieri-Chevalley formula in the K-theory of a 𝐺/𝐵-bundle	1999	Harsh Pittie Arun Ram	10
+ PDF Chat	Kirillov–Reshetikhin crystals for nonexceptional types	2009	Ghislain Fourier Masato Okado Anne Schilling	10
+	Combinatorial Models for Weyl Characters	2002	John R. Stembridge	10
+	Kostka polynomials and energy functions in solvable lattice models	1997	Atsushi Nakayashiki Yasuhiro Yamada	10
+ PDF Chat	Galleries, Hall-Littlewood polynomials, and structure constants of the spherical Hecke algebra	2006	Christoph Schwer	9
+ PDF Chat	Crystals and coboundary categories	2006	André Henriques Joel Kamnitzer	9
+	On the Combinatorics of Crystal Graphs, I	2005	Cristian Lenart	9
+ PDF Chat	Crystal energy functions via the charge in types A and C	2012	Cristian Lenart Anne Schilling	9
+	Crystal bases of modified quantized enveloping algebra	1994	Masaki Kashiwara	9
+ PDF Chat	A uniform model for Kirillov―Reshetikhin crystals	2013	Cristian Lenart Satoshi Naito Daisuke Sagaki Anne Schilling Mark Shimozono	9
+ PDF Chat	Representations of Yangians and multiplicities of occurrence of the irreducible components of the tensor product of representations of simple Lie algebras	1990	A. N. Kirillov Nicolai Reshetikhin	9
+ PDF Chat	Kostka-Foulkes Polynomials Cyclage Graphs and Charge Statistic for the Root System Cn	2005	Cédric Lecouvey	9
+	Some characterizations of Bruhat ordering on a Coxeter group and determination of the relative M�bius function	1977	Vinay V. Deodhar	9
+ PDF Chat	Tensor Product Structure of Affine Demazure Modules and Limit Constructions	2006	Ghislain Fourier Peter Littelmann	9
+ PDF Chat	Quantum cohomology of G/P and homology of affine Grassmannian	2010	Thomas Lam Mark Shimozono	9