Related papers: Character sheaves for symmetric pairs: spin groups
Let D be a connected component of a reductive group over an algebraically closed field. We define a surjective map from the unipotent character sheaves on D to the set of strata of D, extending an earlier result which applied to connected…
We present an overview of the close analogies between the character rings of finite groups and the fusion rings of rational conformal models, which follow from general principles related to orbifold deconstruction.
Homological mirror symmetry predicts that there is a relation between autoequivalence groups of derived categories of coherent sheaves on Calabi-Yau varieties, and the symplectic mapping class groups of symplectic manifolds. In this paper,…
This paper defines and develops cycle indices for the finite classical groups. These tools are then applied to study properties of a random matrix chosen uniformly from one of these groups. Properties studied by this technique will include…
Given a cuspidal automorphic representation of GL(2) over a global function field, we establish a comprehensive cuspidality criterion for symmetric powers. The proof is via passage to the Galois side, possible over function fields thanks to…
We give a construction of cyclic cocycles on convolution algebras twisted by gerbes over discrete translation groupoids. For proper \'etale groupoids, Tu and Xu provide a map between the periodic cyclic cohomology of a gerbe-twisted…
We give closed product formulas for the irreducible characters of the symmetric groups related to rectangular `almost square' Young diagrams $p \times(p+\delta)$ for a fixed value of an integer $\delta$ and an arbitrary integer $p$.
This paper focuses on identifying vertex characteristics in 2D images using topological asymptotic analysis. Vertex characteristics include both the location and the type of the vertex, with the latter defined by the number of lines forming…
We prove that $(\mathbb{Z}_k \wr \mathcal{S}_n \times \mathbb{Z}_k \wr \mathcal{S}_{n-1}, \text{diag} (\mathbb{Z}_k \wr \mathcal{S}_{n-1}) )$ is a symmetric Gelfand pair, where $\mathbb{Z}_k \wr \mathcal{S}_n$ is the wreath product of the…
We investigate the relationship between the symmetric, exterior and classical cohomologies of groups. The first two theories were introduced respectively by Staic and Zarelua. We show in particular, that there is a map from exterior…
A special type of conjugacy classes in symmetric groups is studied and used to answer a question about odd-degree irreducible characters
Coherent sheaves on general complex manifolds do not necessarily have resolutions by finite complexes of vector bundles. However D. Toledo and Y.L.L. Tong showed that one can resolve coherent sheaves by objects analogous to chain complexes…
A general formalism of the relation between geometric phases produced by circularly evolving interacting spin systems and their criticality behavior is presented. This opens up the way for the use of geometric phases as a tool to study…
We study some properties of the characteristic cycle of a constructible complex on a smooth variety over a perfect field, push-forward and product.
For a group $G$ and a subset $X$ of $G$, the commuting graph of $X$, denoted by $\Gamma(G,X)$ is the graph whose vertex set is $X$ and any two vertices $u$ and $v$ in $X$ are adjacent if and only if they commute in $G$. In this article,…
We associate to outer automorphisms of generalized Kac-Moody algebras generalized character-valued indices, the twining characters. A character formula for twining characters is derived which shows that they coincide with the ordinary…
It is shown that four-dimensional generalized symmetric spaces can be naturally equipped with some additional structures defined by means of their curvature operators. As an application, those structures are used to characterize generalized…
The convolution of indicators of two conjugacy classes on the symmetric group S_q is usually a complicated linear combination of indicators of many conjugacy classes. Similarly, a product of the moments of the Jucys--Murphy element involves…
This work focuses on the combinatorial properties of glued semigroups and provides its combinatorial characterization. Some classical results for affine glued semigroups are generalized and some methods to obtain glued semigroups are…
A smooth cuboid can be identified with a $3\times 3$ matrix of linear forms, with coefficients in a field $K$, whose determinant describes a smooth cubic in the projective plane. To each such matrix one can associate a group scheme over…