Séminaire Lotharingien de Combinatoire, B54Ar (2006), 14 pp.
François Descouens and Alain Lascoux
Non-Symmetric Hall-Littlewood Polynomials
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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