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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.


A formula for the $R$-matrix using a system of weight preserving endomorphisms
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by Peter Tingley
Represent. Theory 14 (2010), 435-445
Published electronically: June 3, 2010


We give a formula for the universal $R$-matrix of the quantized universal enveloping algebra $U_q(\mathfrak {g}).$ This is similar to a previous formula due to Kirillov-Reshetikhin and Levendorskii-Soibelman, except that where they use the action of the braid group element $T_{w_0}$ on each representation $V$, we show that one can instead use a system of weight preserving endomorphisms. One advantage of our construction is that it is well defined for all symmetrizable Kac-Moody algebras. However, we have only established that the result is equal to the universal $R$-matrix in finite type.
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Bibliographic Information
  • Peter Tingley
  • Affiliation: Massachusetts Institute of Technology, Department of Mathematics, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139
  • MR Author ID: 679482
  • Email:
  • Received by editor(s): February 24, 2008
  • Published electronically: June 3, 2010
  • Additional Notes: This work was supported by the RTG grant DMS-0354321.
  • © Copyright 2010 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Represent. Theory 14 (2010), 435-445
  • MSC (2010): Primary 17B37; Secondary 16Txx
  • DOI:
  • MathSciNet review: 2652074