Related papers: Character sheaves for classical symmetric pairs

We present a brief summary of the recent discovery of direct tensorial analogue of characters. We distinguish three degrees of generalization: (1) $c$-number Kronecker characters made with the help of symmetric group characters and…

We develop a general theory of canonical bases for quantum symmetric pairs $(\mathbf{U}, \mathbf{U}^\imath)$ with parameters of arbitrary finite type. We construct new canonical bases for the simple integrable $\mathbf{U}$-modules and their…

A new family of asymmetric matrices of Walsh-Hadamard type is introduced. We study their properties and, in particular, compute their determinants and discuss their eigenvalues. The invertibility of these matrices implies that certain…

We give a modern introduction to the moduli of sheaves. After reviewing the classical theory, we give a catalogue of results from the last decade. We then consider a more "symmetric" formulation of the theory by working with gerbes from the…

A classical result of Littlewood gives a factorisation for the Schur function at a set of variables "twisted" by a primitive $t$-th root of unity, characterised by the core and quotient of the indexing partition. While somewhat neglected,…

The notion of pairable functions is introduced and some of its properties are developed. In this connection the famous Euler identity is interpreted as a property of certain pairable functions and finite cyclic groups.

The multisymplectic description of Classical Field Theories is revisited, including its relation with the presymplectic formalism on the space of Cauchy data. Both descriptions allow us to give a complete scheme of classification of…

We give some properties of skew spectrum of a graph, especially, we answer negatively a problem concerning the skew characteristic polynomial and matching polynomial in [M. Cavers et al., Skew-adjacency matrices of graphs, Linear Algebra…

We combine the theory of traces in homotopical algebra with sheaf theory in derived algebraic geometry to deduce general fixed point and character formulas. The formalism of dimension (or Hochschild homology) of a dualizable object in the…

For certain tame abelian covers of arithmetic surfaces X/Y we obtain striking formulas, involving a quadratic form derived from intersection numbers, for the equivariant Euler characteristics of both the canonical sheaf !X/Y and also its…

Let $G = GL(V)$ for an N-dimensional vector space $V$ over an algebraically closed field k, and $G^{\theta}$ the fixed point subgroup of $G$ under an involution $\theta$ on $G$. In the case where $G^{\theta} = O(V)$, the generalized…

This paper concerns character sheaves of connected reductive algebraic groups defined over non-Archimedean local fields and their relation with characters of smooth representations. Although character sheaves were devised with characters of…

The classical Peter-Weyl theorem describes the structure of the space of functions on a semi-simple algebraic group. On the level of characters (in type A) this boils down to the Cauchy identity for the products of Schur polynomials. We…

We use a plethystic formula of Littlewood to answer a question of Miller on embeddings of symmetric group characters. We also reprove a result of Miller on character congruences.

The representation theory of the symmetric groups is intimately related to geometry, algebraic combinatorics, and Lie theory. The spin representation theory of the symmetric groups was originally developed by Schur. In these lecture notes,…

We present a conjecture (and a proof for G=SL(2)) generalizing a result of J. Arthur which expresses a character value of a cuspidal representation of a $p$-adic group as a weighted orbital integral of its matrix coefficient. It also…

We associate a two-sided cell to any (parabolic) character sheaf. We study the interaction of the duality operator for character sheaves and the operation of "twisted induction".

In this paper, we derive some interesting symmetric properties for the geenralized Euler numbers and polynomials.

Let A be a character sheaf on a reductive connected group G over an algebraically closed field. Assuming that the characteristic is not bad, we show that for certain conjugacy classes D in G the restriction of A to D is a local system up to…

The purpose of this work is to provide details about the construction of the Chern character for categorical sheaves mentioned in our previous work "Chern character, loop spaces and derived algebraic geometry". For this, we introduce and…