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Representation Theory

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Harish-Chandra modules for Yangians

Authors: Vyacheslav Futorny, Alexander Molev and Serge Ovsienko
Journal: Represent. Theory 9 (2005), 426-454
MSC (2000): Primary 17B35, 81R10, 17B67
Published electronically: June 2, 2005
MathSciNet review: 2142818
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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

Alexander Molev
Affiliation: School of Mathematics and Statistics, University of Sydney, NSW 2006, Australia

Serge Ovsienko
Affiliation: Faculty of Mechanics and Mathematics, Kiev Taras Shevchenko University, Vladimirskaya 64, 00133, Kiev, Ukraine

Received by editor(s): May 25, 2003
Published electronically: June 2, 2005
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.