A $q$-version of the relation between the hypercube, the Krawtchouk chain and Dicke states

Pierre-Antoine Bernard, Étienne Poliquin, Luc Vinet

It is shown how the spin chain based on the dual $q$-Krawtchouk polynomials is connected to a weighted hypercube through the use of $q$-Dicke states. The representation theoretic u…