Related papers: Character sheaves for symmetric pairs: spin groups

The characteristic map for the symmetric group is an isomorphism relating the representation theory of the symmetric group to symmetric functions. An analogous isomorphism is constructed for the symmetric space of symplectic forms over a…

We study a class of perverse sheaves on some spherical varieties which include the strata of the De Concini-Procesi completion of a symmetric variety. This is a generalization of the theory of (parabolic) character sheaves.

We classify the unipotent character sheaves on a fixed connected component of a reductive algebraic group under a mild hypothesis on the characteristic of the ground field.

The irreducible spin character values of the wreath products of the hyperoctahedral groups with an arbitrary finite group are determined.

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…

We relate character theory of the symmetric groups $S_{2n}$ and $S_{2n+1}$ with that of the hyperoctahedral group $B_n = ({\mathbb Z}/2)^n \rtimes S_n$, as part of the expectation that the character theory of reductive groups with diagram…

We present a nearby cycle sheaf construction in the context of symmetric spaces. This construction can be regarded as a replacement for the Grothendieck-Springer resolution in classical Springer theory.

The paper concerns the automorphism groups of Cayley graphs over cyclic groups which have a rational spectrum (rational circulant graphs for short). With the aid of the techniques of Schur rings it is shown that the problem is equivalent to…

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 continue the study of character sheaves on a reductive group G. To each subset of the set of simple reflections in the Weyl group we associate an algebra of the same kind as an Iwahori-Hecke algebra with unequal parameters…

The irreducible character values of the spin wreath products of the symmetric group and an arbitrary finite group are completely determined.

The symmetric group on a set acts transitively on its subsets of a given size. We define homomorphisms between the corresponding permutation modules, defined over a field of characteristic two, which generalize the boundary maps from…

We provide a purely local computation of the (elliptic) twisted (by "transpose-inverse") character of the representation \pi=I(\1) of PGL(3) over a p-adic field induced from the trivial representation of the maximal parabolic subgroup. This…

We introduce group crosscoders, an extension of crosscoders that systematically discover and analyse symmetrical features in neural networks. While neural networks often develop equivariant representations without explicit architectural…

We relate a generic character sheaf on a disconnected reductive group with a character of a representation of the rational points of the group over a finite field extending a result known in the connected case.

The characters $\chi(\pi)$ of $S_n$ that depend only on the number of cycles of $\pi$ are completely determined.

The main purpose of this paper is to describe a symmetry in the set genuine parameters for even rank nonlinear Spin groups in type B at certain half-integral infinitesimal characters. This symmetry is used to establish a duality of the…

We give classifications of linear orbits of pairs of square matrices with non-vanishing discriminant polynomials over a field in terms of certain coherent sheaves with additional data on closed subschemes of the projective line. Our results…

Finite connected cubic symmetric graphs of girth 6 have been classified by K. Kutnar and D. Maru\v{s}i\v{c}, in particular, each of these graphs has an abelian automorphism group with two orbits on the vertex set. In this paper all cubic…

We study the homology of simplicial and cubical sets with symmetries. These are simplicial and cubical sets with additional maps expressing the symmetries of simplices and cubes. We consider the chain complex computing the homology groups…