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Non-Symmetric Hall-Littlewood Polynomials

Francois Descouens·Alain Lascoux
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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 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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Francois Descouens, Alain Lascoux. 2006-09-19. Non-Symmetric Hall-Littlewood Polynomials. https://arxiv.org/abs/math/0609512

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