Ribbon Tableaux and the Heisenberg Algebra

Details Ribbon Tableaux and the Heisenberg Algebra Ribbon Tableaux and the Heisenberg Algebra

2003-10-16

arxiv.org/abs/math/0310250v2

Mathematics

Quantum Algebra

44 pages. Some corrections and additions. References updated

Scientific paper

Lascoux, Leclerc and Thibon have introduced symmetric functions which are spin and weight generating functions for ribbon tableaux. This article is aimed at studying these `ribbon functions' in analogy with Schur functions. In particular we will describe ribbon Pieri and Murnagham-Nakayama formulae, a ribbon Cauchy identity and an algebra involution which `conjugates' the ribbon functions. We will study these functions in the context of the action of the Heisenberg algebra on the Fock space representation of the quantum affine algebra U_q(sl_n)^, discovered by Kashiwara, Miwa and Stern. We will also connect our formulae with the ribbon insertion of Shimozono and White, giving combinatorial proofs for the domino n=2 case.

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