Weight-dependent commutation relations and combinatorial identities

Abstract

We derive combinatorial identities for variables satisfying specific systems of commutation relations, in particular elliptic commutation relations. The identities thus obtained extend corresponding ones for $q$-commuting variables $x$ and $y$ satisfying $yx=qxy$. In particular, we obtain weight-dependent binomial theorems, functional equations for generalized exponential functions, we derive results for an elliptic derivative of elliptic commuting variables, and finally study weight-dependent extensions of the Weyl algebra which we connect to rook theory.

References in corpus (1)

• Wick's theorem for q-deformed boson operators

Cited by in corpus (4)

• Elliptic Determinantal Processes and Elliptic Dyson Models
• Elliptic and $q$-Analogs of the Fibonomial Numbers
• Elliptic solutions of dynamical Lucas sequences
• Excursion Processes Associated with Elliptic Combinatorics