Séminaire Lotharingien de Combinatoire, B54Ar (2006), 14 pp.

François Descouens and Alain Lascoux

Non-Symmetric Hall-Littlewood Polynomials

Abstract. Using the action of the Yang-Baxter elements of the Hecke algebra on polynomials, we define two bases of polynomials in n variables. The Hall-Littlewood polynomials are a subfamily of one of them. For q=0, these bases specialize to the two families of classical Key polynomials (i.e., Demazure characters for type A). We give a scalar product for which the two bases are adjoint to each other.

Received: September 22, 2006. Accepted: November 3, 2006. Final Version: November 10, 2006.

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