Loewy structure of G₁T-Verma modules of singular highest weights

2015/01/28 by Noriyuki Abe, Abe, Noriyuki, Masaharu Kaneda +1
Mathematics · #20G05 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #math.RT #msc:20G05

paper · pdf · doi:10.48550/arxiv.1501.07029

12 pages

openalex publication_date 2015/01/28 · arxiv created 2015/04/01 · arxiv updated 2015/04/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a reductive algebraic group over an algebraically closed field of positive characteristic, G₁ the Frobenius kernel of G, and T a maximal torus of G. We show that the G₁T-Verma modules of singular highest weights are all rigid, determine their Loewy length, and describe their Loewy structure using the periodic Kazhdan-Lusztig Q-polynomials. We assume that the characteristic of the field is large enough that, in particular, Lusztig's conjecture for the irreducible G₁T-characters hold.

Citations

• Localization of modules for a semisimple Lie algebra in prime characteristic

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