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

Abstract. 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 (C^v₁,C₁). Using this module, we define non-symmetric dual q-Krawtchouk polynomials and describe their orthogonality relations.

Received: November 14, 2016. Accepted: February 17, 2017. Final version: April 1, 2017.

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