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

Abstract It is shown how the spin chain based on dual q -Krawtchouk polynomials is connected to a weighted hypercube through the use of q -Dicke states. The representation theoretic underpinnings based on the quantum algebra <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>U</mml:mi> <mml:mi>q</mml:mi> </mml:msub> <mml:mo stretchy="false">(</mml:mo> <mml:mrow> <mml:mi mathvariant="fraktur">su</mml:mi> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mn>2</mml:mn> <mml:mo stretchy="false">)</mml:mo> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> are emphasized.