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Ribbon Tableaux and the Heisenberg Algebra

Thomas Lam
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Abstract

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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Thomas Lam. 2003-11-10. Ribbon Tableaux and the Heisenberg Algebra. https://arxiv.org/abs/math/0310250

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