Hunt's Formula for $S{U}_q(N)$ and $U_q(N)$

Abstract

We provide a Hunt type formula for the infinitesimal generators of Lévy process on the quantum groups $S{U}_q(N)$ and $U_q(N)$. In particular, we obtain a decomposition of such generators into a gaussian part and a `jump type' part determined by a linear functional that resembles the functional induced by the Lévy measure. The jump part on $S{U}_q(N)$ decomposes further into parts that live on the quantum subgroups $S{U}_q(n)$, $n\le N$. Like in the classical Hunt formula for locally compact Lie groups, the ingredients become unique once a certain projection is chosen. There are analogous result for $U_q(N)$.

45 pages. Except for this comment, this version (v2) coincides with the first version (v1). We wish to emphasize that the published version (see the journal-ref below) differs considerably from this preprint version; see Footnote 1 in the published version

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