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Representation Theory

Published by the American Mathematical Society since 1997, this electronic-only journal is devoted to research in representation theory and seeks to maintain a high standard for exposition as well as for mathematical content. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.71.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Equivalence of a tangle category and a category of infinite dimensional $\mathrm {U}_q(\mathfrak {sl}_2)$-modules
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by K. Iohara, G. I. Lehrer and R. B. Zhang
Represent. Theory 25 (2021), 265-299
Published electronically: April 20, 2021


It is very well known that if $V$ is the simple $2$-dimensional representation of $\mathrm {U}_q(\mathfrak {sl}_2)$, the category of representations $V^{\otimes r}$, $r=0,1,2,\dots$, is equivalent to the Temperley-Lieb category $\mathrm {TL}(q)$. Such categorical equivalences between tangle categories and categories of representations are rare. In this work we give a family of new equivalences by extending the above equivalence to one between the category of representations $M\otimes V^{\otimes r}$, where $M$ is a projective Verma module of $\mathrm {U}_q(\mathfrak {sl}_2)$ and the type $B$ Temperley-Lieb category $\mathbb {TLB}(q,Q)$, realised as a subquotient of the tangle category of Freyd, Yetter, Reshetikhin, Turaev and others.
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Bibliographic Information
  • K. Iohara
  • Affiliation: Univ Lyon, Université Claude Bernard Lyon 1, CNRS UMR 5208, Institut Camille Jordan, 43 Boulevard du 11 Novembre 1918, F-69622 Villeurbanne cedex, France
  • MR Author ID: 334495
  • ORCID: 0000-0001-6748-8256
  • Email:
  • G. I. Lehrer
  • Affiliation: School of Mathematics and Statistics, University of Sydney, N.S.W. 2006, Australia
  • MR Author ID: 112045
  • ORCID: 0000-0002-7918-7650
  • Email:
  • R. B. Zhang
  • Affiliation: School of Mathematics and Statistics, University of Sydney, N.S.W. 2006, Australia
  • Email:
  • Received by editor(s): November 20, 2019
  • Received by editor(s) in revised form: November 25, 2020
  • Published electronically: April 20, 2021
  • Additional Notes: Partially supported by the Australian Research Council.
  • © Copyright 2021 American Mathematical Society
  • Journal: Represent. Theory 25 (2021), 265-299
  • MSC (2020): Primary 17B37, 20G42; Secondary 81R50
  • DOI:
  • MathSciNet review: 4245314