Michael Bate

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All published works

Action	Title	Year	Authors
+ PDF Chat	Geometric rigidity of simple modules for algebraic groups	2024	Michael Bate David I. Stewart
+ PDF Chat	On good $A_1$ subgroups, Springer maps, and overgroups of distinguished unipotent elements in reductive groups	2024	Michael Bate Sören Böhm Benjamin Martin Gerhard Roehrle
+ PDF Chat	The subgroup structure of pseudo-reductive groups	2024	Michael Bate Benjamin Martin Gerhard Röhrle Damian Sercombe
+	A Construction of Pseudo-reductive Groups with Non-reduced Root Systems	2024	Michael Bate Gerhard Röhrle Damian Sercombe David I. Stewart
+ PDF Chat	$G$-complete reducibility and saturation	2024	Michael Bate Sören Böhm Alastair Litterick Benjamin Martin Gerhard Roehrle
+ PDF Chat	Complete reducibility for Lie subalgebras and semisimplification	2023	Michael Bate Sören Böhm Benjamin Martin Gerhard Röhrle Laura Voggesberger
+ PDF Chat	Edifices: building-like spaces associated to linear algebraic groups	2023	Michael Bate Benjamin Martin Gerhard Röhrle
+	Complete reducibility for Lie subalgebras and semisimplification	2023	Michael Bate Sören Böhm Benjamin Martin Gerhard Roehrle Laura Voggesberger
+	Homology of matching complexes and representations of symmetric groups	2023	Michael Bate Brent Everitt Sam Ford
+ PDF Chat	Overgroups of regular unipotent elements in reductive groups	2022	Michael Bate Benjamin Martin Gerhard Röhrle
+	A construction of pseudo-reductive groups with non-reduced root system	2022	Michael Bate Gerhard Röhrle Damian Sercombe David I. Stewart
+ PDF Chat	Irreducible modules for pseudo-reductive groups	2021	Michael Bate David I. Stewart
+ PDF Chat	Cutoff for a one-sided transposition shuffle	2021	Michael Bate Stephen B. Connor Oliver Matheau-Raven
+	Overgroups of regular unipotent elements in reductive groups	2021	Michael Bate Benjamin Martin Gerhard Roehrle
+ PDF Chat	ON RELATIVE COMPLETE REDUCIBILITY	2020	Christopher Attenborough Michael Bate Maike Gruchot Alastair Litterick Gerhard Röhrle
+ PDF Chat	Semisimplification for subgroups of reductive algebraic groups	2020	Michael Bate Benjamin Martin Gerhard Röhrle
+	Cutoff for a One-sided Transposition Shuffle	2019	Michael Bate Stephen B. Connor Oliver Matheau-Raven
+ PDF Chat	On Unipotent Radicals of Pseudo-Reductive Groups	2019	Michael Bate Benjamin Martin Gerhard Röhrle David I. Stewart
+ PDF Chat	Orbit closures and invariants	2019	Michael Bate Haralampos Geranios Benjamin Martin
+	Cutoff for a One-sided Transposition Shuffle	2019	Michael Bate Stephen B. Connor Oliver Matheau-Raven
+	Relative $GL(V)$-complete reducibility	2018	Michael Bate Maike Gruchot Gerhard Roehrle
+	On relative complete reducibility	2018	Christopher Attenborough Michael Bate Maike Gruchot Alastair Litterick Gerhard Roehrle
+	On relative complete reducibility	2018	Christopher Attenborough Michael Bate Maike Gruchot Alastair Litterick Gerhard Roehrle
+	Irreducible modules for pseudo-reductive groups	2017	Michael Bate David I. Stewart
+ PDF Chat	Mixing time and cutoff for a random walk on the ring of integers mod $n$	2017	Michael Bate Stephen B. Connor
+	On unipotent radicals of pseudo-reductive groups	2017	Michael Bate Benjamin Martin Gerhard Roehrle David I. Stewart
+ PDF Chat	ASYMPTOTIC BOUNDS FOR THE SIZE OF Hom(<i>A</i>, GL<sub><i>n</i></sub>(<i>q</i>))	2017	Michael Bate Alec Gullon
+	Irreducible modules for pseudo-reductive groups	2017	Michael Bate David I. Stewart
+	On unipotent radicals of pseudo-reductive groups	2017	Michael Bate Benjamin Martin Gerhard Roehrle David I. Stewart
+ PDF Chat	Cocharacter-closure and the rational Hilbert–Mumford Theorem	2016	Michael Bate Sebastian Herpel Benjamin Martin Gerhard Röhrle
+ PDF Chat	On a question of Külshammer for representations of finite groups in reductive groups	2016	Michael Bate Benjamin Martin Gerhard Röhrle
+	Orbit Closures and Invariants	2016	Michael Bate Haralampos Geranios Benjamin Martin
+	Orbit Closures and Invariants	2016	Michael Bate Haralampos Geranios Benjamin Martin
+ PDF Chat	Cocharacter-closure and spherical buildings	2015	Michael Bate Sebastian Herpel Benjamin Martin Gerhard Röhrle
+	Cocharacter-closure and spherical buildings	2015	Michael Bate Sebastian Herpel Benjamin Martin Gerhard Roehrle
+	On a question of K\"ulshammer for representations of finite groups in reductive groups	2015	Michael Bate Benjamin Martin Gerhard Röhrle
+	On a question of Külshammer for representations of finite groups in reductive groups	2015	Michael Bate Benjamin Martin Gerhard Röhrle
+	Cocharacter-closure and spherical buildings	2015	Michael Bate Sebastian Herpel Benjamin Martin Gerhard Roehrle
+	Cocharacter-closure and the rational Hilbert-Mumford Theorem	2014	Michael Bate Sebastian Herpel Benjamin Martin Gerhard Roehrle
+ PDF Chat	$G$-complete reducibility in non-connected groups	2014	Michael Bate Sebastian Herpel Benjamin Martin Gerhard Röhrle
+	Mixing Time and Cutoff for a Random Walk on the Ring of Integers mod $n$	2014	Michael Bate Stephen B. Connor
+	Cutoff for a Random Walk on the Integers mod $n$	2014	Michael Bate Stephen B. Connor
+	Asymptotic Bounds for the Size of Hom$(A,{\rm GL}_n(q))$	2014	Michael Bate Alec Gullon
+	Asymptotic Bounds for the Size of Hom$(A,{\rm GL}_n(q))$	2014	Michael Bate Alec Gullon
+	Cocharacter-closure and the rational Hilbert-Mumford Theorem	2014	Michael Bate Sebastian Herpel Benjamin Martin Gerhard Roehrle
+	Mixing Time and Cutoff for a Random Walk on the Ring of Integers mod $n$	2014	Michael Bate Stephen B. Connor
+	G-complete reducibility in non-connected groups	2013	Michael Bate Sebastian Herpel Benjamin Martin Gerhard Roehrle
+	G-complete reducibility in non-connected groups	2013	Michael Bate Sebastian Herpel Benjamin Martin Gerhard Roehrle
+ PDF Chat	Closed orbits and uniform $S$-instability in geometric invariant theory	2012	Michael Bate Benjamin Martin Gerhard Röhrle Rudolf Tange
+	The strong Centre Conjecture: An invariant theory approach	2012	Michael Bate Benjamin Martin Gerhard Röhrle
+	Closed H-orbits in G-varieties	2012	Michael Bate
+ PDF Chat	<i>G</i> -complete reducibility and semisimple modules	2011	Michael Bate Sebastian Herpel Benjamin Martin Gerhard Röhrle
+ PDF Chat	Complete reducibility and conjugacy classes of tuples in algebraic groups and Lie algebras	2010	Michael Bate Benjamin Martin Gerhard Röhrle Rudolf Tange
+	The strong Centre Conjecture: an invariant theory approach	2010	Michael Bate Benjamin Martin Gerhard Roehrle
+ PDF Chat	Complete reducibility and separable field extensions	2010	Michael Bate Benjamin Martin Gerhard Röhrle
+	Complete reducibility and separability	2010	Michael Bate Benjamin Martin Gerhard Röhrle Rudolf Tange
+	Complete reducibility and separable field extensions	2010	Michael Bate Benjamin Martin Gerhard Roehrle
+	$G$-complete reducibility and semisimple modules	2010	Michael Bate Sebastian Herpel Benjamin Martin Gerhard Roehrle
+	The strong Centre Conjecture: an invariant theory approach	2010	Michael Bate Benjamin Martin Gerhard Roehrle
+	Complete reducibility and separable field extensions	2010	Michael Bate Benjamin Martin Gerhard Roehrle
+	Closed Orbits and uniform S-instability in Invariant Theory	2009	Michael Bate Benjamin Martin Gerhard Roehrle Rudolf Tange
+ PDF Chat	On Tits' Centre Conjecture for fixed point subcomplexes	2009	Michael Bate Benjamin Martin Gerhard Röhrle
+	Complete Reducibility and Conjugacy classes of tuples in Algebraic Groups and Lie algebras	2009	Michael Bate Benjamin Martin Gerhard Roehrle Rudolf Tange
+	Closed Orbits and uniform S-instability in Geometric Invariant Theory	2009	Michael Bate Benjamin Martin Gerhard Roehrle Rudolf Tange
+ PDF Chat	Optimal Subgroups and Applications to Nilpotent Elements	2008	Michael Bate
+	Subject Guides: History at Murdoch University Library: Statistics	2008	Michael Bate
+ PDF Chat	Complete reducibility and commuting subgroups	2008	Michael Bate Benjamin Martin Gerhard Röhrle
+	On Tits' Centre Conjecture for Fixed Point Subcomplexes	2008	Michael Bate Benjamin Martin Gerhard Roehrle
+	Optimal Subgroups and Applications to Nilpotent Elements	2007	Michael Bate
+	Complete Reducibility and Separability	2007	Michael Bate Benjamin Martin Gerhard Roehrle Rudolf Tange
+	The number of homomorphisms from finite groups to classical groups	2006	Michael Bate
+	Complete Reducibility and Commuting Subgroups	2006	Michael Bate Benjamin Martin Gerhard Roehrle
+ PDF Chat	A geometric approach to complete reducibility	2005	Michael Bate Benjamin Martin Gerhard Röhrle

Common Coauthors

Coauthor	Papers Together
Benjamin Martin	47
Gerhard Roehrle	26
Gerhard Röhrle	24
Sebastian Herpel	11
David I. Stewart	9
Stephen B. Connor	7
Rudolf Tange	7
Sören Böhm	4
Alastair Litterick	4
Maike Gruchot	4
Damian Sercombe	3
Oliver Matheau-Raven	3
Haralampos Geranios	3
Christopher Attenborough	3
Alec Gullon	3
Laura Voggesberger	2
Brent Everitt	1
Sam Ford	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+ PDF Chat	A geometric approach to complete reducibility	2005	Michael Bate Benjamin Martin Gerhard Röhrle	36
+	Complete reducibility and separability	2010	Michael Bate Benjamin Martin Gerhard Röhrle Rudolf Tange	22
+	Reductive subgroups of exceptional algebraic groups	1996	Martin W. Liebeck Gary M. Seitz	22
+ PDF Chat	Instability in Invariant Theory	1978	George R. Kempf	21
+ PDF Chat	On orbits of algebraic groups and Lie groups	1982	R. W. Richardson	19
+	Uniform instability in reductive groups.	1978	Wim H. Hesselink	18
+	Reductive subgroups of reductive groups in nonzero characteristic	2003	Benjamin Martin	18
+	Conjugacy classes of n-tuples in Lie algebras and algebraic groups	1988	R. W. Richardson	17
+	Linear Algebraic Groups	1998	T. A. Springer	16
+ PDF Chat	Complete reducibility and commuting subgroups	2008	Michael Bate Benjamin Martin Gerhard Röhrle	16
+	Linear algebraic groups	1966	Armand Borel	15
+ PDF Chat	Complete reducibility and conjugacy classes of tuples in algebraic groups and Lie algebras	2010	Michael Bate Benjamin Martin Gerhard Röhrle Rudolf Tange	15
+ PDF Chat	Closed orbits and uniform $S$-instability in geometric invariant theory	2012	Michael Bate Benjamin Martin Gerhard Röhrle Rudolf Tange	14
+	A normal subgroup of a strongly reductive subgroup is strongly reductive	2003	Benjamin Martin	13
+	Linear Algebraic Groups	1991	Armand Borel	13
+ PDF Chat	Seminar on Algebraic Groups and Related Finite Groups	1970	Armand Borel Rayna J. Carter C. W. Curtis Nagayoshi Iwahori T. A. Springer Richard H. Steinberg	11
+ PDF Chat	Cocharacter-closure and the rational Hilbert–Mumford Theorem	2016	Michael Bate Sebastian Herpel Benjamin Martin Gerhard Röhrle	10
+	1998 Moursund Lectures at the University of Oregon	2003	Jean-Pierre Serre	9
+	Nilpotent Orbits in Representation Theory	2004	Jens Carsten Jantzen	9
+	Conjugacy Classes in Lie Algebras and Algebraic Groups	1967	R. W. Richardson	9
+	Linear Algebraic Groups	1975	James E. Humphreys	8
+	Geometric Invariant Theory	1994	David Mumford John E. Fogarty Frances Kirwan	8
+	The center conjecture for non-exceptional buildings	2006	Bernhard Mühlherr Jacques Tits	8
+	�l�ments unipotents et sous-groupes paraboliques de groupes r�ductifs. I	1971	Armand Borel Jacques Tits	8
+ PDF Chat	Complete reducibility of rational representations of a matric group	1961	Masayoshi Nagata	8
+ PDF Chat	Buildings of Spherical Type and Finite BN-Pairs	1974	Jacques Tits	7
+	Variations on a theme of Steinberg	2003	Martin W. Liebeck Gary M. Seitz	6
+ PDF Chat	Complete reducibility and separable field extensions	2010	Michael Bate Benjamin Martin Gerhard Röhrle	6
+	Étale Slices for Algebraic Transformation Groups in Characteristic <i>p</i>	1985	Peter Bardsley R. W. Richardson	6
+ PDF Chat	Irreducible subgroups of algebraic groups	2004	Martin W. Liebeck	5
+ PDF Chat	On Tits' Centre Conjecture for fixed point subcomplexes	2009	Michael Bate Benjamin Martin Gerhard Röhrle	5
+ PDF Chat	Optimal Subgroups and Applications to Nilpotent Elements	2008	Michael Bate	5
+ PDF Chat	<i>G</i> -complete reducibility and semisimple modules	2011	Michael Bate Sebastian Herpel Benjamin Martin Gerhard Röhrle	5
+	The strong Centre Conjecture: An invariant theory approach	2012	Michael Bate Benjamin Martin Gerhard Röhrle	5
+	Abstract Homomorphisms of Algebraic Groups	1997	Gary M. Seitz	5
+ PDF Chat	The Center Conjecture for Spherical Buildings of Types F 4 and E 6	2011	Bernhard Leeb Carlos Ramos-Cuevas	5
+ PDF Chat	Classes Unipotentes et Sous-groupes de Borel	1982	N. Spaltenstein	5
+ PDF Chat	Nilpotent orbits in good characteristic and the Kempf–Rousseau theory	2003	Alexander Premet	5
+	Pseudo-reductive Groups	2015	Brian Conrad Ofer Gabber Gopal Prasad	5
+ PDF Chat	Completely reducible Lie subalgebras	2007	George J. McNinch	5
+ PDF Chat	The center conjecture for thick spherical buildings	2012	Carlos Ramos-Cuevas	5
+	Closed Orbits and uniform S-instability in Geometric Invariant Theory	2009	Michael Bate Benjamin Martin Gerhard Roehrle Rudolf Tange	5
+ PDF Chat	On unipotent algebraic $G$-groups and $1$-cohomology	2013	David I. Stewart	4
+	Semisimplicity and Tensor Products of Group Representations: Converse Theorems	1997	Jean-Pierre Serre Walter Feit	4
+	A closer look at semistability for singular principal bundles	2004	Alexander Schmitt	4
+	Linearity for actions on vector groups	2013	George J. McNinch	4
+	Geometric methods in representation theory	1982	Hanspeter Kraft	4
+	Separability and complete reducibility of subgroups of the Weyl group of a simple algebraic group of type <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:msub><mml:mrow><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mn>7</mml:mn></mml:mrow></mml:msub></mml:math>	2014	Tomohiro Uchiyama	4
+	Affine Coset Spaces of Reductive Algebraic Groups	1977	R. W. Richardson	4
+	Complete Reducibility and Conjugacy classes of tuples in Algebraic Groups and Lie algebras	2009	Michael Bate Benjamin Martin Gerhard Roehrle Rudolf Tange	4