A tale of two q-deformations: Connecting dual polar graphs and weighted hypercubes

Abstract

Two $q$-analogs of the hypercube graph are introduced and shown to be related through a graph quotient. The roles of the subspace lattice graph, of a twisted primitive element of $U_q\left(\mathrm{su}\left(2\right)\right)$ and of the dual $q$-Krawtchouk polynomials are elaborated upon. This paper is dedicated to Tom Koornwinder.