Séminaire Lotharingien de Combinatoire, 78B.42 (2017), 12 pp.
Jae-Ho Lee and Hajime Tanaka
Dual Polar Graphs, a Nil-DAHA of Rank One, and
Non-Symmetric Dual q-Krawtchouk Polynomials
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
Using this module, we define non-symmetric dual
q-Krawtchouk polynomials and describe their orthogonality
Received: November 14, 2016.
Accepted: February 17, 2017.
Final version: April 1, 2017.
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