Graded Cartan determinants of the symmetric groups

2012/05/01 by Shunsuke Tsuchioka, Tsuchioka, Shunsuke
Mathematics · #20C08 #81R50 #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math.QA #math.RT #msc:20C08 #msc:81R50

paper · pdf · doi:10.48550/arxiv.1205.0185

26 pages

arxiv created 2012/05/01 · arxiv updated 2012/05/02

Abstract

We give the graded Cartan determinants of the symmetric groups. Based on it, we propose a gradation of Hill's conjecture which is equivalent to Külshammer-Olsson-Robinson's conjecture on the generalized Cartan invariants of the symmetric groups.

Related

• Generalised Cartan invariants of symmetric groups
• On graded Cartan invariants of symmetric groups and Hecke algebras
• Elementary divisors of Cartan matrices for symmetric groups
• Cartan Determinants and Shapovalov forms
• Determinantal formulas with major indices