Finite-dimensional Calogero representation of the $q$-differential operator

Details Finite-dimensional Calogero representation of the $q$-differential operator Finite-dimensional Calogero representation of the $q$-differential operator

1995-04-24

arxiv.org/abs/q-alg/9504021v1

Mathematics

Quantum Algebra

5 pages, LaTeX

Scientific paper

A finite-dimensional matrix representation of the Jackson $q$-differential
operator $D_q$, defined by $D_qf(x)$ $=$ $(f(qx)-f(x))/(x(q-1))$, is written
down following Calogero. Such a representation of $D_q$ should have
applications in $q$-analysis leading to the corresponding extensions of the
numerous results of Calogero's work.

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