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
DOI:
https://doi.org/10.1090/S0273-0979-09-01277-4
Published electronically:
October 27, 2009
MathSciNet review:
2651085
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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
MR Author ID:
268538
Email:
klesh@uoregon.edu
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.
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American Mathematical Society
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