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arXiv · 2009.06323

Hunt's Formula for $SU_q(N)$ and $U_q(N)$

Uwe Franz·Anna Kula·J. Martin Lindsay·Michael Skeide
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Abstract

We provide a Hunt type formula for the infinitesimal generators of L\'evy process on the quantum groups $SU_q(N)$ 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 L\'evy measure. The jump part on $SU_q(N)$ decomposes further into parts that live on the quantum subgroups $SU_q(n)$, $n\le N$. 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 $U_q(N)$.

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Uwe Franz, Anna Kula, J. Martin Lindsay, Michael Skeide. 2020-09-14. Hunt's Formula for $SU_q(N)$ and $U_q(N)$. https://doi.org/10.1512/iumj.2023.72.9485

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