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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

On representations of $ U'_q\mathfrak{so}_n$


Author: Hans Wenzl
Journal: Trans. Amer. Math. Soc. 373 (2020), 3295-3322
MSC (2010): Primary 17B37
DOI: https://doi.org/10.1090/tran/7983
Published electronically: February 19, 2020
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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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Hans Wenzl
Affiliation: Department of Mathematics, University of California La Jolla, San Diego, California 92093
Email: hwenzl@ucsd.edu

DOI: https://doi.org/10.1090/tran/7983
Received by editor(s): May 1, 2018
Received by editor(s) in revised form: August 14, 2019
Published electronically: February 19, 2020
Article copyright: © Copyright 2020 American Mathematical Society