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On the restricted Verma modules at the critical level

Authors: Tomoyuki Arakawa and Peter Fiebig
Journal: Trans. Amer. Math. Soc. 364 (2012), 4683-4712
MSC (2010): Primary 17B67; Secondary 81R10
Published electronically: April 18, 2012
MathSciNet review: 2922606
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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.

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Additional Information

Tomoyuki Arakawa
Affiliation: Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan

Peter Fiebig
Affiliation: Department Mathematik, Universität Erlangen-Nürnberg, 91058 Erlangen, Germany

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
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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