Related papers: Character sheaves for symmetric pairs: spin groups

We show relation between sign of Gaussian curvature of cuspidal edge and geometric invariants through types of singularities of Gauss map. Moreover, we define and characterize positivity/negativity of cusps of Gauss maps by geometric…

We consider the rigid monoidal category of character sheaves on a smooth commutative group scheme $G$ over a finite field $k$ and expand the scope of the function-sheaf dictionary from connected commutative algebraic groups to this setting.…

This paper unifies the concept of kinematic mappings by using geometric algebras. We present a method for constructing kinematic mappings for certain Cayley-Klein geometries. These geometries are described in an algebraic setting by the…

In this paper, we calculate characteristic classes for certain quotients of real Stiefel manifolds $V_{n,k}$ and then derive results on certain numerical invariants, such as characteristic rank and skew embedding dimension, for those…

We present a method of computing elements of spin groups in the case of arbitrary dimension. This method generalizes Hestenes method for the case of dimension 4. We use the method of averaging in Clifford's geometric algebra previously…

On a finite-dimensional real vector space, we give a microlocal characterization of (derived) piecewise linear sheaves (PL sheaves) and prove that the triangulated category of such sheaves is generated by sheaves associated with convex…

A parametrization of irreducible unitary representations associated with the regular adjoint orbits of a hyperspecial compact subgroup of a reductive group over a non-dyadic non-archimedean local filed is presented. The parametrization is…

Let $S_n$ denote a symmetric group, $\chi$ an irreducible character of $S_n$, and $g\in S_n$ an element which decomposes into $k$ disjoint cycles, where $1$-cycles are included. Then $|\chi(g)|\le k!$, and this upper bound is sharp for…

We construct nontrivial auto-equivalences of stable module categories for elementary, local symmetric algebras over a field k. These auto-equivalences are modeled after the spherical twists of Seidel and Thomas and the $\mathbb{P}^n$-twists…

In this paper we propose a construction of generic character sheaves on reductive groups over finite local rings at even levels, whose characteristic functions are higher Deligne--Lusztig characters when the parameters are generic. We…

We introduce and study configuration schemes, which are obtained by ``glueing'' usual schemes along closed embeddings. The category of coherent sheaves on a configuration scheme is investigated. Smooth configuration schemes provide…

Linear intersection pairs of linear codes have become of interest due to their nice algebraic properties and wide applications. In this paper, we focus on linear intersection pairs of cyclic codes over finite fields. Some properties of…

In [AG2] we explored the question what symmetric pairs are Gelfand pairs. We introduced the notion of regular symmetric pair and conjectured that all symmetric pairs are regular. This conjecture would imply that many symmetric pairs are…

We calculate the vector spin chirality for $S=1/2$ zigzag spin chains having U(1) symmetry, using the density matrix renormalization group combined with unitary transformation. We then demonstrate the occurrence of the chiral order for the…

Let G be a reductive groups over an algebraically closed field k. Let P^{(i)} be associated parabolic subgroups, and X^{(i)}:=T^*G/P^i. The bounded derived categories of coherent sheaves on X^{(i)} are equivalent, but there is no canonical…

By exploiting relationships between the values taken by ordinary characters of symmetric groups we prove two theorems in the modular representation theory of the symmetric group. 1. The decomposition matrices of symmetric groups in odd…

It is well-known that theta characteristics on smooth plane curves over a field of characteristic different from two are in bijection with certain smooth complete intersections of three quadrics. We generalize this bijection to possibly…

This paper presents a natural generalisation of Saxl conjecture from a Lie-theoretical perspective, which is verified for the exceptional types. For classical types, progress is made using spin representations, revealing connections to…

In this paper, we investigate a family of graphs associated to collections of arcs on surfaces. These {\it multiarc graphs} naturally interpolate between arc graphs and flip graphs, both well studied objects in low dimensional geometry and…

This short note is some obvious mathematical addendum to our papers on Wilson loops on polygon-like contours with circular edges \cite{Dorn:2020meb,Dorn:2020vzj}. Using the technique of osculating spheres and circles we identify the…