Combinatorics for graded Cartan matrices of the Iwahori-Hecke algebra of type A
Masanori Ando, Takeshi Suzuki, Hiro-Fumi Yamada
TL;DR
This paper explores the combinatorial structure of graded Cartan matrices for the Iwahori-Hecke algebra of type A, providing determinant formulas, combinatorial identities, and conjectures on elementary divisors.
Contribution
It introduces new combinatorial descriptions and conjectural formulas for the elementary divisors of the graded Cartan matrix in type A Iwahori-Hecke algebras.
Findings
Determinant formulas for the graded Cartan matrix.
Combinatorial identities derived from these formulas.
A conjecture on the elementary divisors of the matrix.
Abstract
A -analogue of combinatorics concerning the Cartan matrix for the Iwahori-Hecke algebra of type 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.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Combinatorial Mathematics · Advanced Algebra and Geometry