A formula for the matrix using a system of weight preserving endomorphisms
Author:
Peter Tingley
Journal:
Represent. Theory 14 (2010), 435445
MSC (2010):
Primary 17B37; Secondary 16Txx
Published electronically:
June 3, 2010
MathSciNet review:
2652074
Fulltext PDF Free Access
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Abstract: We give a formula for the universal matrix of the quantized universal enveloping algebra This is similar to a previous formula due to KirillovReshetikhin and LevendorskiiSoibelman, 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 KacMoody 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/S108841652010003787
PII:
S 10884165(2010)003787
Received by editor(s):
February 24, 2008
Published electronically:
June 3, 2010
Additional Notes:
This work was supported by the RTG grant DMS0354321.
Article copyright:
© Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
