Harish-Chandra modules for Yangians
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- by Vyacheslav Futorny, Alexander Molev and Serge Ovsienko
- Represent. Theory 9 (2005), 426-454
- DOI: https://doi.org/10.1090/S1088-4165-05-00195-0
- Published electronically: June 2, 2005
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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.References
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Bibliographic 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