On representations of 𝑈’_{𝑞}𝔰𝔬_{𝔫}

Wenzl, Hans

doi:10.1090/tran/7983

On representations of $U’_q\mathfrak {so}_n$
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Trans. Amer. Math. Soc. 373 (2020), 3295-3322 Request permission

Abstract:

We study representations of the non-standard quantum deformation $U’_q\mathfrak {so}_n$ of $U\mathfrak {so}_n$ via a Verma module approach. This is used to recover the classification of finite-dimensional modules for $q$ not a root of unity, given by classical and non-classical series. We obtain new results at roots of unity, including the classification of self-adjoint representations on Hilbert spaces.

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