English

Strong minuscule elements in the finite Weyl groups

Combinatorics 2021-03-15 v2 Representation Theory

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.

Keywords

Cite

@article{arxiv.1904.12979,
  title  = {Strong minuscule elements in the finite Weyl groups},
  author = {Yuki Motegi},
  journal= {arXiv preprint arXiv:1904.12979},
  year   = {2021}
}

Comments

15 pages: We extend the results in the previous version (which was only for type A) to all finite Weyl groups

R2 v1 2026-06-23T08:52:51.550Z