Geodesic
Non-Symmetric Hall-Littlewood Polynomials
Séminaire lotharingien de combinatoire, 54A (2005-2007)

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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. 

@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},
     publisher = {mathdoc},
     volume = {54A},
     year = {2005-2007},
     url = {http://geodesic.mathdoc.fr/item/SLC_2005-2007_54A_a17/}
}
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AU  - Alain Lascoux
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JO  - Séminaire lotharingien de combinatoire
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%F SLC_2005-2007_54A_a17
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/