Non-Symmetric Hall-Littlewood Polynomials

Details Non-Symmetric Hall-Littlewood Polynomials Non-Symmetric Hall-Littlewood Polynomials

2006-09-19

arxiv.org/abs/math/0609512v1

Mathematics

Combinatorics

Dedicated to Adriano Garsia

Scientific paper

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 into 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 of each other.

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