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Fusion procedure for the Brauer algebra


Authors: A. P. Isaev and A. I. Molev
Original publication: Algebra i Analiz, tom 22 (2010), nomer 3.
Journal: St. Petersburg Math. J. 22 (2011), 437-446
MSC (2010): Primary 81R05, 05E10
DOI: https://doi.org/10.1090/S1061-0022-2011-01150-1
Published electronically: March 17, 2011
MathSciNet review: 2729943
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Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that all primitive idempotents for the Brauer algebra $ \mathcal{B}_n(\omega)$ can be found by evaluating a rational function in several variables that has the form of a product of $ R$-matrix type factors. This provides an analog of the fusion procedure for $ \mathcal{B}_n(\omega)$.


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Additional Information

A. P. Isaev
Affiliation: Bogolyubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna 141980, Moscow Region, Russia
Email: isaevap@theor.jinr.ru

A. I. Molev
Affiliation: School of Mathematics and Statistics, University of Sydney, NSW 2006, Australia
Email: alexm@maths.usyd.edu.au

DOI: https://doi.org/10.1090/S1061-0022-2011-01150-1
Keywords: Fusion procedure, Brauer algebra, up-down tableau, Young tableau
Received by editor(s): January 15, 2010
Published electronically: March 17, 2011
Additional Notes: The first author was supported by RFBR (grant no. 08-01-00392-a) and by RFBR-CNRS (grant no. 07-02-92166-a)
Dedicated: Dedicated to L. D. Faddeev on the occasion of his 75th birthday
Article copyright: © Copyright 2011 American Mathematical Society

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