The Decomposition of Permutation Module for Infinite Chevalley Groups

2019/04/17 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.1904.08077

openalex publication_date 2019/04/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let \bf G be a connected reductive group defined over \mathbbF_q, the finite field with q elements. Let \bf B be an Borel subgroup defined over \mathbbF_q. In this paper, we completely determine the composition factors of the induced module \mathbbM(\optr)=\Bbbk\bf G⊗_\Bbbk\bf B\optr (\optr is the trivial \bf B-module) for any field \Bbbk.

Citations

• On the principal series representations of semisimple groups with Frobenius maps
• Irreducibility of Certain Subquotients of Spherical Principal Series Representations of Reductive Groups with Frobenius Maps

Related

• The Permutation Module on Flag Varieties in Cross Characteristic
• Abstract induced modules for reductive algebraic groups with Frobenius maps
• The block decomposition of the principal representation category of reductive algebraic groups with Frobenius maps
• Irreducible Modules of Reductive Groups with Borel-stable Line
• Bounded complexes of permutation modules