Crystal graphs, Tokuyama's theorem, and the Gindikin--Karpelevic formula for G₂

2014/02/03 by Holley Friedlander, Friedlander, Holley, Louis Gaudet +3
Mathematics · #05E15 #20C15 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #Primary 17B10 #Representation Theory (math.RT) #Secondary 11F68 #math.CO #math.NT #math.RT #msc:05E15 #msc:11F68 #msc:17B10 #msc:20C15

paper · pdf · doi:10.48550/arxiv.1402.0411

arxiv created 2014/02/03 · openalex publication_date 2014/02/03 · arxiv updated 2014/02/04 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

We conjecture a deformation of the Weyl character formula for type G₂ in the spirit of Tokuyama's formula for type A. Using our conjecture we prove a combinatorial version of the Gindikin--Karpelevic formula for G₂, in the spirit of Bump--Nakasuji's formula for type A.

Related

• Crystal constructions in Number Theory
• Lecture notes on Geometric Crystals and their combinatorial analogues
• Combinatorics of canonical bases revisited: Type A
• On the Combinatorics of Crystal Graphs, I. Lusztig's Involution
• A Generalization of Tokuyama's Formula to the Hall-Littlewood Polynomials