Non-Symmetric Hall-Littlewood Polynomials

Francois Descouens (1) , Alain Lascoux (1)

1 LIGM - Laboratoire d'Informatique Gaspard-Monge

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.

Mots clés: Hall-Littlewood polynomials; Demazure characters; Key polynomials

Domaines: Combinatoire [math.CO]

Francois Descouens, Alain Lascoux. Non-Symmetric Hall-Littlewood Polynomials. 2006. ⟨hal-00096385⟩