On dominance and minuscule Weyl group elements

2009/08/07 by Qëndrim R. Gashi, Gashi, Qëndrim R., Travis Schedler +1
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT) #math.CO #math.RT

paper · pdf · doi:10.48550/arxiv.0908.1091

12 pages

arxiv created 2009/08/07 · arxiv updated 2009/12/01

Abstract

Fix a Dynkin diagram and let p be a coweight. When does there exist an element w of the corresponding Weyl group such that w is p-minuscule and w(p) is dominant? We answer this question for general Coxeter groups. We express and prove these results using a variant of Mozes's game of numbers.

Related

• Minimally dominant elements of finite Coxeter groups
• The numbers game, geometric representations of Coxeter groups, and Dynkin diagram classification results
• Punctured surfaces, quiver mutations, and quotients of Coxeter groups
• Strong minuscule elements in the finite Weyl groups
• Quasi-constant fundamental weights in terms of Levi Weyl groups