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arXiv · 1508.07770

An algebraic interpretation of the multivariate $q$-Krawtchouk polynomials

Vincent X. Genest·Sarah Post·Luc Vinet
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Abstract

The multivariate quantum $q$-Krawtchouk polynomials are shown to arise as matrix elements of "$q$-rotations" acting on the state vectors of many $q$-oscillators. The focus is put on the two-variable case. The algebraic interpretation is used to derive the main properties of the polynomials: orthogonality, duality, structure relations, difference equations and recurrence relations. The extension to an arbitrary number of variables is presented

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Vincent X. Genest, Sarah Post, Luc Vinet. 2015-08-31. An algebraic interpretation of the multivariate $q$-Krawtchouk polynomials. https://arxiv.org/abs/1508.07770

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