Geodesic
Dual Polar Graphs, a Nil-DAHA of Rank One, and Non-Symmetric Dual q-Krawtchouk Polynomials
Séminaire lotharingien de combinatoire, 78B (2017)

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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. 

@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},
     publisher = {mathdoc},
     volume = {78B},
     year = {2017},
     url = {http://geodesic.mathdoc.fr/item/SLC_2017_78B_a41/}
}
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AU  - Jae-Ho Lee
AU  - Hajime Tanaka
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JO  - Séminaire lotharingien de combinatoire
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VL  - 78B
PB  - mathdoc
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%0 Journal Article
%A Jae-Ho Lee
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%V 78B
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SLC_2017_78B_a41/
%F SLC_2017_78B_a41
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/