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Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(online) ISSN 0273-0979(print)

 

Representation theory of symmetric groups and related Hecke algebras


Author: Alexander Kleshchev
Journal: Bull. Amer. Math. Soc. 47 (2010), 419-481
MSC (2000): Primary 20C30, 20C08, 17B37, 20C20, 17B67
Published electronically: October 27, 2009
MathSciNet review: 2651085
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Abstract: We survey some fundamental trends in representation theory of symmetric groups and related objects which became apparent in the last fifteen years. The emphasis is on connections with Lie theory via categorification. We present results on branching rules and crystal graphs, decomposition numbers and canonical bases, graded representation theory, connections with cyclotomic and affine Hecke algebras, Khovanov-Lauda-Rouquier algebras, category $ {\mathcal O}$, $ W$-algebras, etc.


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Additional Information

Alexander Kleshchev
Affiliation: Department of Mathematics, University of Oregon, Eugene, Oregon
Email: klesh@uoregon.edu

DOI: http://dx.doi.org/10.1090/S0273-0979-09-01277-4
PII: S 0273-0979(09)01277-4
Received by editor(s): March 30, 2009
Received by editor(s) in revised form: August 17, 2009
Published electronically: October 27, 2009
Additional Notes: Supported in part by the NSF grant DMS-0654147. The paper was completed while the author was visiting the Isaac Newton Institute for Mathematical Sciences in Cambridge, U.K. The author thanks the Institute for hospitality and support.
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.