Michael Schlosser

Affiliation: University of Vienna, Austria

Email: michael.schlosser@univie.ac.at

Title Of Talk: Special commutation relations and combinatorial identities

Abstract: We study commutation relations involving special weight functions, for which we obtain a weight-dependent generalization of the binomial theorem. In the notable special case of the weight functions being suitably chosen elliptic (i.e., doubly-periodic meromorphic) functions, our algebra consists of, what we call, "elliptic-commuting'' variables (which generalize the q-commuting variables with yx=qxy). These are shown to satisfy an elliptic generalization of the binomial theorem. The latter can be utilized to quickly recover Frenkel and Turaev's ₁₀V₉ summation formula, an identity fundamental to the (rather young) theory of elliptic hypergeometric series. Furthermore, the combinatorial interpretation of our commutation relations in terms of weighted lattice paths allows us to deduce other combinatorial identities as well.

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