Combinatorics for graded Cartan matrices of the Iwahori-Hecke algebra of type A

Abstract

A $q$-analogue of combinatorics concerning the Cartan matrix for the Iwahori-Hecke algebra of type $A$ is investigated. We give several descriptions for the determinant of the graded Cartan matrix, which imply some combinatorial identities. A conjectural expression for the elementary divisors is also presented.

18 pages

References in corpus (4)

• A diagrammatic approach to categorification of quantum groups I
• 2-Kac-Moody algebras
• Graded decomposition numbers for cyclotomic Hecke algebras
• Graded cellular bases for the cyclotomic Khovanov-Lauda-Rouquier algebras of type A