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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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