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.
A $q$-version of the relation between the hypercube, the Krawtchouk chain and Dicke states
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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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The Lie algebra $\mathfrak{sl}_4(\mathbb C)$ and the hypercubes
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.