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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.

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Fibers of characters in Gelfand-Tsetlin categories
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by Vyacheslav Futorny and Serge Ovsienko PDF
Trans. Amer. Math. Soc. 366 (2014), 4173-4208 Request permission

Abstract:

For a class of noncommutative rings, called Galois orders, we study the problem of an extension of characters from a commutative subalgebra. We show that for Galois orders this problem is always solvable in the sense that all characters can be extended, moreover, in finitely many ways, up to isomorphism. These results can be viewed as a noncommutative analogue of liftings of prime ideals in the case of integral extensions of commutative rings. The proposed approach can be applied to the representation theory of many infinite dimensional algebras including universal enveloping algebras of reductive Lie algebras (in particular $\mathrm {gl}_n$), Yangians and finite $W$-algebras. As an example we recover the theory of Gelfand-Tsetlin modules for $\mathrm {gl}_n$.
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Additional Information
  • Vyacheslav Futorny
  • Affiliation: Instituto de Matemática e Estatística, Universidade de São Paulo, Caixa Postal 66281, São Paulo, CEP 05315-970, Brasil
  • MR Author ID: 238132
  • Email: futorny@ime.usp.br
  • Serge Ovsienko
  • Affiliation: Faculty of Mechanics and Mathematics, Kiev Taras Shevchenko University, Vladimirskaya 64, 00133, Kiev, Ukraine
  • Email: ovsiyenko.sergiy@gmail.com
  • Received by editor(s): January 19, 2010
  • Received by editor(s) in revised form: June 18, 2010, August 14, 2012, and August 18, 2012
  • Published electronically: April 7, 2014
  • Additional Notes: The first author was supported in part by the CNPq grant (processo 301743/2007-0) and by the Fapesp grant (processo 2010/50347-9)
    The second author is grateful to Fapesp for financial support (processos 2004/02850-2 and 2006/60763-4) and to the University of São Paulo for their hospitality during his visits
  • © Copyright 2014 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 366 (2014), 4173-4208
  • MSC (2010): Primary 16D60, 16D90, 16D70, 17B65
  • DOI: https://doi.org/10.1090/S0002-9947-2014-05938-2
  • MathSciNet review: 3206456