Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Temperley–Lieb, Brauer and Racah algebras and other centralizers of $\mathfrak {su}(2)$
HTML articles powered by AMS MathViewer

by Nicolas Crampé, Loïc Poulain d’Andecy and Luc Vinet PDF
Trans. Amer. Math. Soc. 373 (2020), 4907-4932 Request permission

Abstract:

In the spirit of the Schur–Weyl duality, we study the connections between the Racah algebra and the centralizers of tensor products of three (possibly different) irreducible representations of $\mathfrak {su}(2)$. As a first step we show that the Racah algebra always surjects onto the centralizer. We then offer a conjecture regarding the description of the kernel of the map, which depends on the irreducible representations. If true, this conjecture would provide a presentation of the centralizer as a quotient of the Racah algebra. We prove this conjecture in several cases. In particular, while doing so, we explicitly obtain the Temperley–Lieb algebra, the Brauer algebra and the one-boundary Temperley–Lieb algebra as quotients of the Racah algebra.
References
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 16S20, 17B35
  • Retrieve articles in all journals with MSC (2010): 16S20, 17B35
Additional Information
  • Nicolas Crampé
  • Affiliation: Institut Denis-Poisson CNRS/UMR 7013, Université de Tours, Université d’Orléans, Parc de Grandmont, 37200 Tours, France; and Centre de Recherches Mathématiques, Université de Montréal, P.O. Box 6128, Centre-ville Station, Montréal, Québec, H3C 3J7, Canada
  • Email: crampe1977@gmail.com
  • Loïc Poulain d’Andecy
  • Affiliation: Laboratoire de mathématiques de Reims UMR 9008, Université de Reims Champagne-Ardenne, UFR Sciences exactes et naturelles, Moulin de la Housse BP 1039, 51100 Reims, France
  • Email: loic.poulain-dandecy@univ-reims.fr
  • Luc Vinet
  • Affiliation: Centre de Recherches Mathématiques, Université de Montréal, P.O. Box 6128, Centre-ville Station, Montréal, Québec, H3C 3J7, Canada
  • MR Author ID: 178665
  • ORCID: 0000-0001-6211-7907
  • Email: vinet@CRM.UMontreal.ca
  • Received by editor(s): August 2, 2019
  • Received by editor(s) in revised form: November 4, 2019
  • Published electronically: March 27, 2020
  • Additional Notes: The first and second authors were partially supported by Agence National de la Recherche Projet AHA ANR-18-CE40-0001.
    The research of the third author was supported in part by a Discovery Grant from the Natural Science and Engineering Research Council (NSERC) of Canada.
  • © Copyright 2020 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 373 (2020), 4907-4932
  • MSC (2010): Primary 16S20, 17B35
  • DOI: https://doi.org/10.1090/tran/8055
  • MathSciNet review: 4127866