Anthony Henderson

Weyl group actions on the Springer sheaf

Publisher: Wiley

Date: 11-12-2013

DOI: 10.1112/PLMS/PDT055

Bases for certain cohomology representations of the symmetric group

Publisher: Springer Science and Business Media LLC

Date: 11-07-2006

DOI: 10.1007/S10801-006-0018-3

Modular generalized Springer correspondence II: classical groups

Publisher: European Mathematical Society - EMS - Publishing House GmbH

Date: 2017

DOI: 10.4171/JEMS/687

Diagram automorphisms of quiver varieties

Publisher: Elsevier BV

Date: 12-2014

DOI: 10.1016/J.AIM.2014.08.007

Fourier transform, parabolic induction, and nilpotent orbits

Publisher: Springer Science and Business Media LLC

Date: 12-2001

DOI: 10.1007/BF01237252

Rational cohomology of the real Coxeter toric variety of type A

Publisher: Scuola Normale Superiore

Date: 2012

DOI: 10.1007/978-88-7642-431-1_14

Constructible sheaves on nilpotent cones in rather good characteristic

Publisher: Springer Science and Business Media LLC

Date: 15-04-2016

DOI: 10.1007/S00029-016-0236-Z

The exotic Robinson–Schensted correspondence

Publisher: Elsevier BV

Date: 11-2012

DOI: 10.1016/J.JALGEBRA.2012.06.029

Involutions on the Affine Grassmannian and Moduli Spaces of Principal Bundles

Publisher: Institute of Mathematics, Academia Sinica

Date: 03-2018

DOI: 10.21915/BIMAS.2018103

Corrigendum to “Orbit closures in the enhanced nilpotent cone” [Adv. Math. 219 (1) (2008) 27–62]

Publisher: Elsevier BV

Date: 12-2011

DOI: 10.1016/J.AIM.2011.05.030

The Cohomology of Real De Concini–Procesi Models of Coxeter Type

Publisher: Oxford University Press (OUP)

Date: 2008

DOI: 10.1093/IMRN/RNN001

Symmetric subgroup invariants in irreducible representations of GF, when G=GLn

Publisher: Elsevier BV

Date: 03-2003

DOI: 10.1016/S0021-8693(02)00559-8

Braid groups of normalizers of reflection subgroups

Publisher: Cellule MathDoc/CEDRAM

Date: 07-2022

DOI: 10.5802/AIF.3440

Species Over a Finite Field

Publisher: Springer Science and Business Media LLC

Date: 03-2005

DOI: 10.1007/S10801-005-6905-1

Geometric Satake, Springer correspondence and small representations

Publisher: Springer Science and Business Media LLC

Date: 05-05-2013

DOI: 10.1007/S00029-013-0125-7

Modular generalized Springer correspondence I: the general linear group

Publisher: European Mathematical Society - EMS - Publishing House GmbH

Date: 2016

DOI: 10.4171/JEMS/618

THE SYMMETRIC GROUP REPRESENTATION ON COHOMOLOGY OF THE REGULAR ELEMENTS OF A MAXIMAL TORUS OF THE SPECIAL LINEAR GROUP

Publisher: Cambridge University Press (CUP)

Date: 02-2008

DOI: 10.1017/S1446788708000074

Abstract: We give a formula for the character of the representation of the symmetric group S n on each isotypic component of the cohomology of the set of regular elements of a maximal torus of SL n , with respect to the action of the centre.

Pieces of nilpotent cones for classical groups

Publisher: American Mathematical Society (AMS)

Date: 22-08-2011

DOI: 10.1090/S1088-4165-2011-00393-9

Abstract: We compare orbits in the nilpotent cone of type B n B_n , that of type C n C_n , and Kato’s exotic nilpotent cone. We prove that the number of F q \\mathbb {F}_q -points in each nilpotent orbit of type B n B_n or C n C_n equals that in a corresponding union of orbits, called a type- B B or type- C C piece, in the exotic nilpotent cone. This is a finer version of Lusztig’s result where corresponding special pieces in types B n B_n and C n C_n have the same number of F q \\mathbb {F}_q -points. The proof requires studying the case of characteristic 2 2 , where more direct connections between the three nilpotent cones can be established. We also prove that the type- B B and type- C C pieces of the exotic nilpotent cone are smooth in any characteristic.

Orbit closures in the enhanced nilpotent cone

Publisher: Elsevier BV

Date: 09-2008

DOI: 10.1016/J.AIM.2008.04.008

Normality of orbit closures in the enhanced nilpotent cone

Publisher: Cambridge University Press (CUP)

Date: 09-2011

DOI: 10.1215/00277630-1331854

Abstract: We continue the study of the closures of GL( V )-orbits in the enhanced nilpotent cone V × N begun by the first two authors. We prove that each closure is an invariant-theoretic quotient of a suitably defined enhanced quiver variety. We conjecture, and prove in special cases, that these enhanced quiver varieties are normal complete intersections, implying that the enhanced nilpotent orbit closures are also normal.

Unimodality of Eulerian quasisymmetric functions

Publisher: Elsevier BV

Date: 2012

DOI: 10.1016/J.JCTA.2011.07.004

Nilpotent orbits of linear and cyclic quivers and Kazhdan-Lusztig polynomials of type A

Publisher: American Mathematical Society (AMS)

Date: 26-06-2007

DOI: 10.1090/S1088-4165-07-00317-2

Abstract: The intersection cohomologies of closures of nilpotent orbits of linear (respectively, cyclic) quivers are known to be described by Kazhdan-Lusztig polynomials for the symmetric group (respectively, the affine symmetric group). We explain how to simplify this description using a combinatorial cancellation procedure, and we derive some consequences for representation theory.

The equivariant Euler characteristic of real Coxeter toric varieties

Publisher: Wiley

Date: 07-04-2009

DOI: 10.1112/BLMS/BDP023

Representations of wreath products on cohomology of De Concini-Procesi compactifications

Publisher: Oxford University Press (OUP)

Date: 2004

DOI: 10.1155/S1073792804132510

Plethysm for Wreath Products and Homology of Sub-Posets of Dowling Lattices

Publisher: The Electronic Journal of Combinatorics

Date: 12-10-2006

DOI: 10.37236/1113

Abstract: We prove analogues for sub-posets of the Dowling lattices of the results of Calderbank, Hanlon, and Robinson on homology of sub-posets of the partition lattices. The technical tool used is the wreath product analogue of the tensor species of Joyal.

Induced characters of the projective general linear group over a finite field

Publisher: Elsevier BV

Date: 2007

DOI: 10.1016/J.JALGEBRA.2006.03.005

Exterior powers of the reflection representation in the cohomology of Springer fibres

Publisher: Elsevier BV

Date: 10-2010

DOI: 10.1016/J.CRMA.2010.09.015

Spherical functions of the symmetric space 𝐺(𝔽_{𝕢²})/𝔾(𝔽_{𝕢})

Publisher: American Mathematical Society (AMS)

Date: 28-11-2001

DOI: 10.1090/S1088-4165-01-00119-4

Abstract: We apply Lusztig’s theory of character sheaves to the problem of calculating the spherical functions of G ( F q 2 ) / G ( F q ) G(\\mathbb {F}_{q^{2}})/G(\\mathbb {F}_q) , where G G is a connected reductive algebraic group. We obtain the solution for generic spherical functions for any G G , and for all spherical functions when G = G L n G=GL_n . The proof includes a result about convolution of character sheaves and its interaction with the associated two-sided cells.

Geometric Satake, Springer correspondence, and small representations II

Publisher: American Mathematical Society (AMS)

Date: 18-05-2015

DOI: 10.1090/ERT/465

Abstract: For a split reductive group scheme G ˇ \\check G over a commutative ring k \\Bbbk with Weyl group W W , there is an important functor R e p ( G ˇ , k ) → R e p ( W , k ) {\\mathsf {Rep}}(\\check G,\\Bbbk )\\to {\\mathsf {Rep}}(W,\\Bbbk ) defined by taking the zero weight space. We prove that the restriction of this functor to the subcategory of small representations has an alternative geometric description, in terms of the affine Grassmannian and the nilpotent cone of the Langlands dual group G G . The translation from representation theory to geometry is via the Satake equivalence and the Springer correspondence. This generalizes the result for the k = C \\Bbbk =\\mathbb {C} case proved by the first two authors, and also provides a better explanation than in the earlier paper, since the current proof is uniform across all types.

Two-row nilpotent orbits of cyclic quivers

Publisher: Springer Science and Business Media LLC

Date: 2003

DOI: 10.1007/S00209-002-0455-1

Modular generalized Springer correspondence III: exceptional groups

Publisher: Springer Science and Business Media LLC

Date: 24-02-2017

DOI: 10.1007/S00208-017-1524-4

Department Of Defence, Australian Government

Location: No location found

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University Of Sydney

Location: Australia

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Massachusetts Institute Of Technology

Location: United States of America

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Department Of Defence, Australian Government

Location: Australia

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Discovery Projects - Grant ID: DP0986349

Start Date: 01-2009

End Date: 12-2016

Amount: $428,000.00

Funder: Australian Research Council

Discovery Projects - Grant ID: DP0985184

Start Date: 02-2009

End Date: 06-2011

Amount: $40,000.00

Funder: Australian Research Council

Discovery Projects - Grant ID: DP170101579

Start Date: 2017

End Date: 06-2021

Amount: $345,000.00

Funder: Australian Research Council

Discovery Projects - Grant ID: DP0344185

Start Date: 2003

End Date: 12-2006

Amount: $226,900.00

Funder: Australian Research Council

Discovery Projects - Grant ID: DP160103897

Start Date: 2016

End Date: 2024

Amount: $519,300.00

Funder: Australian Research Council

ARC Future Fellowships - Grant ID: FT110100504

Start Date: 2012

End Date: 07-2016

Amount: $660,776.00

Funder: Australian Research Council