The Permutation Module on Flag Varieties in Cross Characteristic

2017/07/09 by Xiaoyu Chen, Chen, Xiaoyu, Junbin Dong +1
Mathematics · #20G05 #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1707.02592

openalex publication_date 2017/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let \bf G be a connected reductive group over \mathbbF_q, the algebraically closure of \mathbbF_q (the finite field with q=p^e elements), with the standard Frobenius map F. Let \bf B be an F-stable Borel subgroup. Let \Bbbk be a field of characteristic r≠ p. In this paper, we completely determine the composition factors of the induced module Ind_B^Gtr=\BbbkG⊗_\Bbbk\bf B tr (here \BbbkH is the group algebra of the group H, and tr is the trivial B-module). In particular, we find a new family of infinite dimensional irreducible abstract representations of G.

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