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Periods of Deligne-Lusztig Characters associated to Spherical Varieties

Fang Shi

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.

Periods of Deligne-Lusztig Characters associated to Spherical Varieties

Abstract

In this paper, we calculate the periods of Deligne-Lusztig characters associated to , where for a connected spherical subgroup of . As an application, we deduce a formula that partially generalizes Lusztig's work on symmetric spaces and extends Reeder's formula in the complexity case.
Paper Structure (34 sections, 49 theorems, 92 equations)

This paper contains 34 sections, 49 theorems, 92 equations.

Table of Contents

  1. Introduction
  2. An overview
  3. Structure of this paper
  4. Conventions
  5. Transporters of semisimple elements
  6. Transporters with reduced scheme structure
  7. $\mathrm k$-points of $\mathrm T(t,H)$
  8. A partition of $T$
  9. The Multiplicity Formula
  10. Functions of geometric type
  11. Summation on $G^F$
  12. Deligne-Lusztig characters
  13. Flag variety
  14. Periods of Deligne-Lusztig characters
  15. Periods of Deligne-Lusztig characters
  16. ...and 19 more sections

Key Result

Theorem 1.3

Suppose that the assumption $\star$ is fulfilled. Let $T$ and $\chi$ be as above. We have

Theorems & Definitions (141)

  • Definition 1.1
  • Definition 1.2
  • Theorem 1.3
  • Remark 1.4
  • Theorem 1.5
  • Lemma 2.1
  • proof
  • Remark 2.2
  • Proposition 2.3
  • proof
  • ...and 131 more