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

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arxiv 2408.14388 v1 pith:ECTLYTFT submitted 2024-08-26 math-ph math.MPquant-ph

Pierre-Antoine Bernard , Étienne Poliquin , Luc Vinet This is my paper · ORCID
classification math-phmath.MPquant-ph
keywords chaindickehypercubekrawtchoukstatesalgebraconnecteddual
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abstract

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 underpinnings based on the quantum algebra $U_q(\mathfrak{su}(2))$ are emphasized.

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  1. The Lie algebra $\mathfrak{sl}_4(\mathbb C)$ and the hypercubes

    math.CO 2025-05 conditional novelty 7.0 of 10

    The degree-N polynomials in four variables, the fixed 3-tensors of the hypercube, and the hypercube Terwilliger algebra are all isomorphic as sl4(C)-modules, with explicit maps.

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