PBW Filtration and Bases for Symplectic Lie Algebras

Evgeny Feigin, Ghislain Fourier, Peter Littelmann

Type: Article

Publication Date: 2011-01-01

Citations: 66

DOI: https://doi.org/10.1093/imrn/rnr014

Abstract

We study the PBW filtration on the highest weight representations V (λ) of ⁠. This filtration is induced by the standard degree filtration on ⁠. We give a description of the associated graded -module gr V (λ) in terms of generators and relations. We also construct a basis of gr V (λ). As an application we derive a graded combinatorial formula for the character of V (λ) and obtain a new class of bases of the modules V (λ).

Locations

International Mathematics Research Notices - View
arXiv (Cornell University) - View - PDF

Similar Works

Action	Title	Year	Authors
+	PBW filtration and bases for symplectic Lie algebras	2010	Evgeny Feigin Ghislain Fourier Peter Littelmann
+	PBW filtration and bases for symplectic Lie algebras	2010	Evgeny Feigin Ghislain Fourier Peter Littelmann
+	Monomial bases and PBW filtration in representation theory	2016	Teodor Backhaus
+	PBW-filtration over ℤ and Compatible Bases for V ℤ(λ) in Type A n and C n	2012	Evgeny Feigin Ghislain Fourier Peter Littelmann
+	PBW filtration and bases for irreducible modules in type $A_n$	2010	Evgeny Feigin Ghislain Fourier Peter Littelmann
+	The PBW filtration	2007	Evgeny Feigin
+	The PBW filtration	2007	Evgeny Feigin
+ PDF Chat	PBW filtration and monomial bases for Demazure modules in types A and C	2022	George Balla Ghislain Fourier Kunda Kambaso
+	PBW filtration: Feigin-Fourier-Littelmann modules via Hasse diagrams	2014	Teodor Backhaus Christian Desczyk
+	FFLV polytopes for odd symplectic Lie algebras	2021	Д. С. Рыбин
+	PBW--filtration over $\bz$ and compatible bases for $V_\bz(\la)$ in type ${\tt A}_n$ and ${\tt C}_n$	2012	Evgeny Feigin Ghislain Fourier Peter Littelmann
+	PBW--filtration over $\bz$ and compatible bases for $V_\bz(\la)$ in type ${\tt A}_n$ and ${\tt C}_n$	2012	Evgeny Feigin Ghislain Fourier Peter Littelmann
+	PBW filtration and bases for irreducible modules in type A n	2010	Evgeny Feigin Ghislain Fourier Peter Littelmann
+	Z-bases and Hilbert-Poincaré polynomials related to PBW filtrations	2015	Christian Desczyk
+	The PBW filtration	2009	Evgeny Feigin
+	The PBW filtration and convex polytopes in type $\tt B$	2015	Teodor Backhaus Deniz Kus
+	The PBW filtration and convex polytopes in type $\tt B$	2015	Teodor Backhaus Deniz Kus
+	PBW-basis for universal enveloping algebras of differential graded Poisson algebras	2017	Xianguo Hu Jiafeng Lü Xingting Wang
+	FFLV polytopes for odd symplectic Lie algebras	2021	Д. С. Рыбин
+ PDF Chat	PBW-Basis for Universal Enveloping Algebras of Differential Graded Poisson Algebras	2018	Xianguo Hu Jiafeng Lü Xingting Wang

Works That Cite This (64)

Action	Title	Year	Authors
+ PDF Chat	The degree of the Hilbert–Poincaré polynomial of PBW-graded modules	2014	Teodor Backhaus Lara Bossinger Christian Desczyk Ghislain Fourier
+ PDF Chat	Gelfand–Tsetlin polytopes and Feigin–Fourier–Littelmann–Vinberg polytopes as marked poset polytopes	2011	Federico Ardila Thomas Bliem Dido Salazar
+ PDF Chat	Parabolic contractions of semisimple Lie algebras and their invariants	2013	Dmitri I. Panyushev Oksana Yakimova
+ PDF Chat	GELFAND–TSETLIN DEGENERATIONS OF REPRESENTATIONS AND FLAG VARIETIES	2020	Igor Makhlin
+ PDF Chat	Newton–Okounkov Bodies of Flag Varieties and Combinatorial Mutations	2020	Naoki Fujita Akihiro Higashitani
+ PDF Chat	DEGREE CONES AND MONOMIAL BASES OF LIE ALGEBRAS AND QUANTUM GROUPS	2017	Teodor Backhaus Xin Fang Ghislain Fourier
+	PBW Degeneration: Algebra, Geometry, and Combinatorics	2018	Evgeny Feigin
+ PDF Chat	Marked poset polytopes: Minkowski sums, indecomposables, and unimodular equivalence	2015	Ghislain Fourier
+	Marked chain-order polytopes	2016	Xin Fang Ghislain Fourier
+ PDF Chat	Semi-infinite Plücker Relations and Weyl Modules	2018	Evgeny Feigin Ievgen Makedonskyi

Works Cited by This (16)

Action	Title	Year	Authors
+	Introduction to Lie Algebras and Representation Theory	1972	James E. Humphreys
+ PDF Chat	A $\phi_{1,3}$-Filtration of the Virasoro Minimal Series $M(p, p')$ with $1 < p'/p < 2$	2008	Boris Feigin Evgeny Feigin M. Jimbo Tetsuji Miwa Yoshihiro Takeyama
+	The PBW filtration	2009	Evgeny Feigin
+	Limits of weight spaces, Lusztig’s 𝑞-analogs, and fiberings of adjoint orbits	1989	Ranee Brylinski
+ PDF Chat	Gelfand–Tsetlin polytopes and Feigin–Fourier–Littelmann–Vinberg polytopes as marked poset polytopes	2011	Federico Ardila Thomas Bliem Dido Salazar
+ PDF Chat	The Nil Hecke Ring and Singularity of Schubert Varieties	1994	Shrawan Kumar
+ PDF Chat	The PBW Filtration, Demazure Modules and Toroidal Current Algebras	2008	Evgeny Feigin
+	Zhu's algebra, the C_2 algebra, and twisted modules	2008	Matthias R. Gaberdiel Terry Gannon
+	PBW filtration and bases for irreducible modules in type A n	2010	Evgeny Feigin Ghislain Fourier Peter Littelmann
+	Tensor product multiplicities and convex polytopes in partition space	1988	Arkady Berenstein Andrei Zelevinsky