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Representation Theory

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ISSN 1088-4165

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Harish-Chandra modules for Yangians
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by Vyacheslav Futorny, Alexander Molev and Serge Ovsienko PDF
Represent. Theory 9 (2005), 426-454 Request permission

Abstract:

We study Harish-Chandra representations of the Yangian $\mathrm {Y}(\mathfrak {gl}_2)$ with respect to a natural maximal commutative subalgebra. We prove an analogue of the Kostant theorem showing that the restricted Yangian $\mathrm {Y}_p(\mathfrak {gl}_2)$ is a free module over the corresponding subalgebra $\Gamma$ and show that every character of $\Gamma$ defines a finite number of irreducible Harish-Chandra modules over $\mathrm {Y}_p(\mathfrak {gl}_2)$. We study the categories of generic Harish-Chandra modules, describe their simple modules and indecomposable modules in tame blocks.
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Additional Information
  • Vyacheslav Futorny
  • Affiliation: Institute of Mathematics and Statistics, University of São Paulo, Caixa Postal 66281-CEP 05315-970, São Paulo, Brazil
  • MR Author ID: 238132
  • Email: futorny@ime.usp.br
  • Alexander Molev
  • Affiliation: School of Mathematics and Statistics, University of Sydney, NSW 2006, Australia
  • MR Author ID: 207046
  • Email: alexm@maths.usyd.edu.au
  • Serge Ovsienko
  • Affiliation: Faculty of Mechanics and Mathematics, Kiev Taras Shevchenko University, Vladimirskaya 64, 00133, Kiev, Ukraine
  • Email: ovsienko@sita.kiev.ua
  • Received by editor(s): May 25, 2003
  • Published electronically: June 2, 2005
  • © Copyright 2005 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Represent. Theory 9 (2005), 426-454
  • MSC (2000): Primary 17B35, 81R10, 17B67
  • DOI: https://doi.org/10.1090/S1088-4165-05-00195-0
  • MathSciNet review: 2142818