arXiv subjects

Guy Kapon

Publications and source records attributed to Guy Kapon.

6 recordsLinked to original sources

arXiv2026

On Representations of Weyl Groups attached to Spherical Varieties

To any smooth spherical $G$ variety $X$ we attach two representations of the Weyl group of $G$. The first is constructed geometrically using Borel Moore homology. The second is constructed combinatorially using the structure of the Borel orbits on $X$. Using the Fourier Sato transform, we show that both representations are isomorphic. We use this result to translate (in the cotangent case) a conjecture of Finkelberg-Ginzburg-Travkin in the relative Langlands program to a combinatorial problem. We solve this combinatorial problem for several examples.

math.RT↗

arXiv2026

Betti Numbers of Negatively Curved Orbifolds with Coefficients in Arbitrary Fields

We show that the Betti numbers of finite-volume negatively curved orbifolds grow at most linearly with the volume, with coefficients in an arbitrary field. In particular, this gives a linear bound for the Betti numbers of finite-volume hyperbolic orbifolds over $\mathbb{F}_p$. This extends a theorem of Gromov from manifolds to orbifolds in negative curvature, and answers a question of Samet, by strengthening his theorem from characteristic $0$ to arbitrary characteristic. The key new input is a quantitative bound on the homology of spherical quotients.

math.GT↗

arXiv2025

Distinguished Representations with respect to Symmetric Subgroups of $GL_{n}(\mathbb{F}_{q})$

We study representations of $GL_{n}(\mathbb{F}_{q})$ that are distinguished with respect to a symmetric subgroup $H=GL_{n}(\mathbb{F}_{q})^σ$, where $σ$ is an involution. We prove that those representations satisfy $π\cong π^{*,σ}$, thus positively answering a version of the Prasad-Lapid conjecture.

math.RT↗

arXiv2022

Distinguished Representations of $\mathrm{GL}_{n}(\mathbb{F}_{q})$

Let $\mathrm{G} = \mathrm{Gl}_{n}(K)$, and $\mathrm{H} = \mathrm{G}^σ$ for $σ$ an involution of the form $g\rightarrow aga^{-1}$, It is known that for $K =\mathbb{Q}_q$ any irreducible representation of $\mathrm{G}$ with an $\mathrm{H}$ invariant functional, is self dual, we prove an analogous result for $\mathbb{F}_{q}$.

math.RT↗

arXiv2022

Characterising Semi-Simple Lie Algebras by Their Borel Nilpotent Radical

We show that semi-simple lie algebras can be characterized by their maximal nilpotent subalgebra, which is the same as the nilpotent radical of a Borel subalgebra.

math.RA↗

arXiv2019

Singularity Properties of Graph Varieties

For a graph $G=(V,E)$, and a symplectic vector space $(W, \left<\cdot,\cdot\right>)$, we define a variety $X(G,W)$ consisting of all functions $w:V\to W$ satisfying $\left = 0$ for any edge $\{u,v\}$ in $G$. We study the singularities of this varieties.

math.AG↗