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On the restricted Verma modules at the critical level

We study the restricted Verma modules of an affine Kac-Moody algebra at the critical level with special emphasis on their Jordan-H"older multiplicities. The Feigin-Frenkel conjecture gives 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.

preprint2010arXivOpen access
Tomoyuki ArakawaPeter Fiebig
math.RT
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Tomoyuki ArakawaPeter Fiebig

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