An algebraic interpretation of the multivariate $q$-Krawtchouk polynomials
Classical Analysis and ODEs
2015-12-15 v2 Mathematical Physics
math.MP
Quantum Algebra
Abstract
The multivariate quantum -Krawtchouk polynomials are shown to arise as matrix elements of "-rotations" acting on the state vectors of many -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
Cite
@article{arxiv.1508.07770,
title = {An algebraic interpretation of the multivariate $q$-Krawtchouk polynomials},
author = {Vincent X. Genest and Sarah Post and Luc Vinet},
journal= {arXiv preprint arXiv:1508.07770},
year = {2015}
}
Comments
22 pages; minor corrections