Ribbon Tableaux and the Heisenberg Algebra
Thomas Lam
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 Uq(sln), 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.
Create a lesson
Related papers
An Explicit Construction of Commuting Quantum KdV Hamiltonians in the Universal Virasoro Vertex Algebra
Hongbo Zhao
Vertex Operator Algebras in Lean: a formal library and its companion book
Fedor K. Popov, Leonardo Rastelli
Uniform localization and boundary corrections for two-node quiver Coulomb branches
Xiaomin Tang
Property F and weak integrality of braided fusion categories
Enyu Li, Yuze Ruan
From the quantum group Uq1/2( sl2 ) to the Kronecker quantum cluster algebra
Junyuan Huang, Xueqing Chen, Ming Ding et al.
C2-Cofiniteness of Permutation Orbifolds I: Relative C1 Descent
Yuhan Gu, Jiancai Sun