Geodesic
Dual Polar Graphs, a Nil-DAHA of Rank One, and Non-Symmetric Dual q-Krawtchouk Polynomials
Séminaire lotharingien de combinatoire, 78B (2017) 
Jae-Ho Lee; Hajime Tanaka. Dual Polar Graphs, a Nil-DAHA of Rank One, and Non-Symmetric Dual q-Krawtchouk Polynomials. Séminaire lotharingien de combinatoire, 78B (2017). http://geodesic.mathdoc.fr/item/SLC_2017_78B_a41/
@article{SLC_2017_78B_a41,
     author = {Jae-Ho Lee and Hajime Tanaka},
     title = {Dual {Polar} {Graphs,} a {Nil-DAHA} of {Rank} {One,} and {Non-Symmetric} {Dual} {q-Krawtchouk} {Polynomials}},
     journal = {S\'eminaire lotharingien de combinatoire},
     year = {2017},
     volume = {78B},
     url = {http://geodesic.mathdoc.fr/item/SLC_2017_78B_a41/}
}
TY  - JOUR
AU  - Jae-Ho Lee
AU  - Hajime Tanaka
TI  - Dual Polar Graphs, a Nil-DAHA of Rank One, and Non-Symmetric Dual q-Krawtchouk Polynomials
JO  - Séminaire lotharingien de combinatoire
PY  - 2017
VL  - 78B
UR  - http://geodesic.mathdoc.fr/item/SLC_2017_78B_a41/
ID  - SLC_2017_78B_a41
ER  - 
%0 Journal Article
%A Jae-Ho Lee
%A Hajime Tanaka
%T Dual Polar Graphs, a Nil-DAHA of Rank One, and Non-Symmetric Dual q-Krawtchouk Polynomials
%J Séminaire lotharingien de combinatoire
%D 2017
%V 78B
%U http://geodesic.mathdoc.fr/item/SLC_2017_78B_a41/
%F SLC_2017_78B_a41

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

Let Γ be a dual polar graph with diameter D >= 3. From every pair of a vertex of Γ and a maximal clique containing it, we construct a 2D-dimensional irreducible module for a nil-DAHA of type (Cv1,C1). Using this module, we define non-symmetric dual q-Krawtchouk polynomials and describe their orthogonality relations.