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Representation Theory
Representation Theory
ISSN 1088-4165

 

Centers of degenerate cyclotomic Hecke algebras and parabolic category $ \mathcal O$


Author: Jonathan Brundan
Journal: Represent. Theory 12 (2008), 236-259
MSC (2000): Primary 20C08, 17B20
Published electronically: July 29, 2008
MathSciNet review: 2424964
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Abstract: We prove that the center of each degenerate cyclotomic Hecke algebra associated to the complex reflection group of type $ B_d(l)$ consists of symmetric polynomials in its commuting generators. The classification of the blocks of the degenerate cyclotomic Hecke algebras is an easy consequence. We then apply Schur-Weyl duality for higher levels to deduce analogous results for parabolic category $ \mathcal O$ for the Lie algebra $ \mathfrak{gl}_n(\mathbb{C})$.


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Additional Information

Jonathan Brundan
Affiliation: Department of Mathematics, University of Oregon, Eugene, Oregon 97403
Email: brundan@uoregon.edu

DOI: http://dx.doi.org/10.1090/S1088-4165-08-00333-6
PII: S 1088-4165(08)00333-6
Received by editor(s): August 15, 2006
Received by editor(s) in revised form: June 25, 2008
Published electronically: July 29, 2008
Additional Notes: Research supported in part by NSF grant no. DMS-0654147.
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.