On the restricted Verma modules at the critical level
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- by Tomoyuki Arakawa and Peter Fiebig PDF
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Abstract:
We study the restricted Verma modules of an affine Kac–Moody algebra at the critical level with a special emphasis on their Jordan–Hölder multiplicities. Feigin and Frenkel conjectured a formula for these multiplicities that involves the periodic Kazhdan–Lusztig polynomials. We prove this conjecture for all subgeneric blocks and for the case of anti-dominant simple subquotients.References
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Additional Information
- Tomoyuki Arakawa
- Affiliation: Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan
- MR Author ID: 611463
- Email: arakawa@kurims.kyoto-u.ac.jp
- Peter Fiebig
- Affiliation: Department Mathematik, Universität Erlangen-Nürnberg, 91058 Erlangen, Germany
- Email: fiebig@mi.uni-erlangen.de
- Received by editor(s): June 4, 2010
- Received by editor(s) in revised form: September 17, 2010
- Published electronically: April 18, 2012
- Additional Notes: The first author was partially supported by the JSPS Grant-in-Aid for Scientific Research (B) No. 20340007.
The second author was supported by a grant of the Landesstiftung Baden–Württemberg - © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 364 (2012), 4683-4712
- MSC (2010): Primary 17B67; Secondary 81R10
- DOI: https://doi.org/10.1090/S0002-9947-2012-05467-5
- MathSciNet review: 2922606