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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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
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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
Email: arakawa@kurims.kyoto-u.ac.jp

Peter Fiebig
Affiliation: Department Mathematik, Universität Erlangen-Nürnberg, 91058 Erlangen, Germany
Email: fiebig@mi.uni-erlangen.de

DOI: http://dx.doi.org/10.1090/S0002-9947-2012-05467-5
PII: S 0002-9947(2012)05467-5
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.