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Levi-spherical Schubert varieties

Yibo Gao, Reuven Hodges, Alexander Yong

Abstract

We prove a short, root-system uniform, combinatorial classification of Levi-spherical Schubert varieties for any generalized flag variety $G/B$ of finite Lie type. We apply this to the study of multiplicity-free decompositions of a Demazure module into irreducible representations of a Levi subgroup.

Levi-spherical Schubert varieties

Abstract

We prove a short, root-system uniform, combinatorial classification of Levi-spherical Schubert varieties for any generalized flag variety of finite Lie type. We apply this to the study of multiplicity-free decompositions of a Demazure module into irreducible representations of a Levi subgroup.
Paper Structure (9 sections, 12 theorems, 36 equations)

This paper contains 9 sections, 12 theorems, 36 equations.

Table of Contents

  1. Introduction
  2. History and motivation
  3. Background
  4. The main result
  5. Organization
  6. Examples of Theorem \ref{['conj:main']}
  7. An equivariant isomorphism
  8. Proof of the main result
  9. Application to Demazure modules

Key Result

Theorem 1.3

Fix $w\in W$ and $I\subseteq {\mathcal{D}}_L(w)$. $X_w$ is $L_I$-spherical if and only if $w$ is $I$-spherical.

Theorems & Definitions (27)

  • Definition 1.1: Hodges.Yong1
  • Definition 1.2
  • Theorem 1.3
  • Example 2.1: $E_8$ cf. Hodges.Yong1
  • Example 2.2: $F_4$ cf. Hodges.Yong1
  • Example 2.3: $D_4$
  • Lemma 3.1
  • proof
  • Lemma 3.2
  • proof
  • ...and 17 more