A formula for the -matrix using a system of weight preserving endomorphisms

Author:
Peter Tingley

Journal:
Represent. Theory **14** (2010), 435-445

MSC (2010):
Primary 17B37; Secondary 16Txx

Published electronically:
June 3, 2010

MathSciNet review:
2652074

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Abstract | References | Similar Articles | Additional Information

Abstract: We give a formula for the universal -matrix of the quantized universal enveloping algebra 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 on each representation , 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 -matrix in finite type.

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Additional Information

**Peter Tingley**

Affiliation:
Massachusetts Institute of Technology, Department of Mathematics, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139

Email:
ptingley@math.mit.edu

DOI:
http://dx.doi.org/10.1090/S1088-4165-2010-00378-7

Received by editor(s):
February 24, 2008

Published electronically:
June 3, 2010

Additional Notes:
This work was supported by the RTG grant DMS-0354321.

Article copyright:
© Copyright 2010
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.