Q-Vandermonde Identity - Other Conventions

Other Conventions

As is typical for q-analogues, the q-Vandermonde identity can be rewritten in a number of ways. In the conventions common in applications to quantum groups, a different q-binomial coefficient is used. This q-binomial coefficient, which we denote here by, is defined by . (In particular, it is the unique shift of the "usual" q-binomial coefficient by a power of q such that the result is symmetric in q and .) Using this q-binomial coefficient, the q-Vandermonde identity can be written in the form

B_q(m + n,k) = q^{n k} \sum_{j} q^{-(m+n)j} B_q(m,k - j) B_q(n,j). \,

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