Ribbon Schur Operators

Abstract

A new combinatorial approach to the ribbon tableaux generating functions and q-Littlewood Richardson coefficients of Lascoux, Leclerc and Thibon is suggested. We define operators which add ribbons to partitions and following Fomin and Greene study non-commutative symmetric functions in these operators. This allows us to give combinatorial interpretations for some (skew) q-Littlewood Richardson coefficients whose non-negativity appears not to be known. Our set up also leads to a new proof of the action of the Heisenberg algebra on the Fock space of U_q(sl^_n) due to Kashiwara, Miwa and Stern.