Combinatorics for Graded Cartan Matrices of the Iwahori-Hecke Algebra of Type A

Combinatorics concerning graded Cartan matrices 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.