Geodesic
Non-Symmetric Hall-Littlewood Polynomials
Séminaire lotharingien de combinatoire, 54A (2005-2007) 
François Descouens; Alain Lascoux. Non-Symmetric Hall-Littlewood Polynomials. Séminaire lotharingien de combinatoire, 54A (2005-2007). http://geodesic.mathdoc.fr/item/SLC_2005-2007_54A_a17/
@article{SLC_2005-2007_54A_a17,
     author = {Fran\c{c}ois Descouens and Alain Lascoux},
     title = {Non-Symmetric {Hall-Littlewood} {Polynomials}},
     journal = {S\'eminaire lotharingien de combinatoire},
     year = {2005-2007},
     volume = {54A},
     url = {http://geodesic.mathdoc.fr/item/SLC_2005-2007_54A_a17/}
}
TY  - JOUR
AU  - François Descouens
AU  - Alain Lascoux
TI  - Non-Symmetric Hall-Littlewood Polynomials
JO  - Séminaire lotharingien de combinatoire
PY  - 2005-2007
VL  - 54A
UR  - http://geodesic.mathdoc.fr/item/SLC_2005-2007_54A_a17/
ID  - SLC_2005-2007_54A_a17
ER  - 
%0 Journal Article
%A François Descouens
%A Alain Lascoux
%T Non-Symmetric Hall-Littlewood Polynomials
%J Séminaire lotharingien de combinatoire
%D 2005-2007
%V 54A
%U http://geodesic.mathdoc.fr/item/SLC_2005-2007_54A_a17/
%F SLC_2005-2007_54A_a17

Voir la notice de l'acte provenant de la source Séminaire Lotharingien de Combinatoire website

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.