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). \,

Read more about this topic:  Q-Vandermonde Identity

Famous quotes containing the word conventions:

    “Languages exist by arbitrary institutions and conventions among peoples; words, as the dialecticians tell us, do not signify naturally, but at our pleasure.”
    —François Rabelais (1494–1553)

    “It is not human nature we should accuse but the despicable conventions that pervert it.”
    —Denis Diderot (1713–1784)