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Frobenius map for the centers of Hecke algebras


Authors: Jinkui Wan and Weiqiang Wang
Journal: Trans. Amer. Math. Soc. 367 (2015), 5507-5520
MSC (2010): Primary 20C08; Secondary 05E05
DOI: https://doi.org/10.1090/S0002-9947-2014-06211-9
Published electronically: December 18, 2014
MathSciNet review: 3347181
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Abstract: We introduce a commutative associative graded algebra structure on the direct sum $ \mathcal Z$ of the centers of the Hecke algebras associated to the symmetric groups in $ n$ letters for all $ n$. As a natural deformation of the classical construction of Frobenius, we establish an algebra isomorphism from $ \mathcal Z$ to the ring of symmetric functions. This isomorphism provides an identification between several distinguished bases for the centers (introduced by Geck-Rouquier, Jones, Lascoux) and explicit bases of symmetric functions.


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Additional Information

Jinkui Wan
Affiliation: School of Mathematics, Beijing Institute of Technology, Beijing, 100081, People’s Republic of China
Email: wjk302@hotmail.com

Weiqiang Wang
Affiliation: Department of Mathematics, University of Virginia, Charlottesville, Virginia 22904
Email: ww9c@virginia.edu

DOI: https://doi.org/10.1090/S0002-9947-2014-06211-9
Keywords: Hecke algebras, centers, symmetric functions, Frobenius map
Received by editor(s): May 15, 2013
Received by editor(s) in revised form: June 6, 2013
Published electronically: December 18, 2014
Additional Notes: The first author was partially supported by NSFC-11101031, and the second author was partially supported by NSF DMS-1101268
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.