Hunt's formula for SUq(N) and Uq(N)

Franz, Uwe and Kula, Anna and Lindsay, Martin and Skeide, Michael (2023) Hunt's formula for SUq(N) and Uq(N). Indiana University Mathematics Journal, 72 (4). pp. 1717-1748. ISSN 0022-2518

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Abstract

For any Lévy process on the quantum group SUq(N), where 0 < q < 1 and N ∈ N, a Lévy-Khintchine type decomposition of its generating functional is given, together with an analogue of Hunt's formula. The non-gaussian component is shown to further decompose into generating functionals that live on the quantum subgroups SUq(n), for n <= N. Corresponding results are also given for the quantum groups Uq(N).