Strong minuscule elements in the finite Weyl groups

2019/04/29 by Yuki Motegi, Motegi, Yuki
Mathematics · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1904.12979

openalex publication_date 2019/04/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce the notion of a strong minuscule element, and prove that the dominant integral weight associated to a strong minuscule element is the fundamental weight corresponding to a short simple root. In addition, we enumerate the strong minuscule elements explicitly, and then as an application of this enumeration, determine the dimension of certain Demazure modules in the finite-dimensional irreducible modules whose highest weights are minuscule weights.

Related

• Gelfand-Kirillov dimensions and associated varieties of highest weight modules
• Weight polytopes and saturation of Demazure characters
• On dominance and minuscule Weyl group elements
• Quasi-constant fundamental weights in terms of Levi Weyl groups
• Weyl algebra modules