Periods of Deligne-Lusztig Characters associated to Spherical Varieties

2024/09/25 by Fang Shi, Shi, Fang
Mathematics · Computer Science · #Advanced Algebra and Geometry #semigroups and automata theory #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2409.16853

Abstract

In this paper, we calculate the periods of Deligne-Lusztig characters R_T,χ^G associated to X^F, where X=G/H for a connected spherical subgroup H of G. As an application, we deduce a formula that partially generalizes Lusztig's work on symmetric spaces and extends Reeder's formula in the complexity 0 case.

Related

• Periods and harmonic analysis on spherical varieties
• Relative character identities and theta correspondence
• On certain period relations for cusp forms on GL_n
• Periods of Automorphic Forms Associated to Strongly Tempered Spherical Varieties
• Families of Canonical Local Periods on Spherical Varieties