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Related papers: Character sheaves for symmetric pairs: spin groups

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We give an explicit description of character sheaves for the symmetric pairs associated to inner involutions of the special linear groups. We make use of the general strategy given in [VX1] and central character consideration. We also…

Representation Theory · Mathematics 2025-03-25 Kari Vilonen , Ting Xue

We establish a Springer theory for classical symmetric pairs. We give an explicit description of character sheaves in this setting. In particular we determine the cuspidal character sheaves.

Representation Theory · Mathematics 2025-03-25 Kari Vilonen , Ting Xue , with an appendix by Dennis Stanton

In this paper we construct full support character sheaves for stably graded Lie algebras. Conjecturally these are precisely the cuspidal character sheaves. Irreducible representations of Hecke algebras associated to complex reflection…

Representation Theory · Mathematics 2025-03-25 Kari Vilonen , Ting Xue

In this paper we give a complete classification of cyclically graded semisimple Lie algebras that afford cuspidal character sheaves and determine the support of the cuspidal character sheaves. This constitutes a major step towards the…

Representation Theory · Mathematics 2025-12-24 Wille Liu , Kari Vilonen , Ting Xue

We will consider a two dimensional "symmetric" subfamily of the four dimensional family of Fricke cubic surfaces. The main result is that such symmetric cubic surfaces arise as character varieties for the exceptional group of type G_2.…

Algebraic Geometry · Mathematics 2014-10-02 Philip Boalch , Robert Paluba

In 1911 Schur computed the spin character values of the symmetric group using two important ingredients: the first one later became famously known as the Schur Q-functions and the second one was certain creative construction of the…

Group Theory · Mathematics 2014-03-26 Xiaoli Hu , Naihuan Jing

Let X be an exotic symmetric space G/H \times V, where G= GL(V) and H = Sp(V) for a symplectic vector space V over an algebraically closed field of odd characteristic. In our previous papers, character sheaves on X were constructed based on…

Representation Theory · Mathematics 2014-08-01 Toshiaki Shoji , Karine Sorlin

We give a definition of character sheaves on the group compactification which is equivalent to Lusztig's definition in \cite{L3}. We also prove some properties of the character sheaves on the group compactification.

Representation Theory · Mathematics 2007-05-23 Xuhua He

We determine cuspidal character sheaves explicitly for all (GIT) stably graded exceptional Lie algebras.

Representation Theory · Mathematics 2026-05-21 Ting Xue

We continue the study of character sheaves on a not necessarily connected reductive group. We prove orthogonality formulas for certain characteristic functions.

Representation Theory · Mathematics 2007-05-23 G. Lusztig

We show in this paper that in the context of graded Lie algebras, all cuspidal character sheaves arise from a nearby-cycle construction followed by a Fourier--Sato transform in a very specific manner. Combined with results of the last two…

Representation Theory · Mathematics 2025-12-29 Wille Liu , Cheng-Chiang Tsai , Kari Vilonen , Ting Xue

This paper contains an exposition of the theory of character sheaves for reductive groups and some attempts to extend it to other cases: unipotent groups, reductive groups modulo the unipotent radical of a parabolic.

Representation Theory · Mathematics 2007-05-23 G. Lusztig

We give a new formula for the irreducible spin characters of the symmetric groups. This formula is analogous to Stanley's character formula for the usual (linear) characters of the symmetric groups.

Combinatorics · Mathematics 2020-03-03 Sho Matsumoto , Piotr Śniady

In this article we formulate and prove the main theorems of the theory of character sheaves on unipotent groups over an algebraically closed field of characteristic p>0. In particular, we show that every admissible pair for such a group G…

Representation Theory · Mathematics 2013-01-08 Mitya Boyarchenko , Vladimir Drinfeld

We show that some types for supercuspidal representations of tamely ramified $p$-adic groups that appear in Jiu-Kang Yu's work are geometrizable. To do so, we define a function-sheaf dictionary for one-dimensional characters of arbitrary…

Algebraic Geometry · Mathematics 2019-07-04 Clifton Cunningham , David Roe

We develop a characterization for the existence of symmetries of canal surfaces defined by a rational spine curve and rational radius function. In turn, this characterization inspires an algorithm for computing the symmetries of such canal…

Algebraic Geometry · Mathematics 2017-08-15 Juan Gerardo Alcázar , Heidi E. I. Dahl , Georg Muntingh

We define and study convolution of parabolic character sheaves. As an application we attach to any parabolic character sheaf the orbit of a tame local system on the maximal torus under a subgroup of the Weyl group.

Representation Theory · Mathematics 2007-05-23 G. Lusztig

In this paper we introduce a new ingredient, invariant systems of differential equations, to our study of character sheaves on graded Lie algebras. The character sheaves we construct in this paper, together with the ones constructed in…

Representation Theory · Mathematics 2024-10-29 Kari Vilonen , Ting Xue

We study a class of perverse sheaves on the variety of pairs (P,gU_P) where P runs through a conjugacy class of parabolics in a connected reductive group G and gU_P runs through G/U_P. This is a generalization of the theory of character…

Representation Theory · Mathematics 2007-05-23 G. Lusztig

We study asymptotics of characters of the symmetric groups on a fixed conjugacy class. It was proved by Kerov that such a character can be expressed as a polynomial in free cumulants of the Young diagram (certain functionals describing the…

Combinatorics · Mathematics 2012-03-13 Maciej Dołega , Piotr Śniady
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