Michael J. Schlosser and
Meesue Yoo
Weight-dependent commutation relations and combinatorial identities
(24 pages)
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 quasicommuting variables,
and finally study weight-dependent extensions of the Weyl algebra
which we connect to rook theory.
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