On the restricted Verma modules at the critical level

Arakawa, Tomoyuki; Fiebig, Peter

doi:10.1090/S0002-9947-2012-05467-5

On the restricted Verma modules at the critical level
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by Tomoyuki Arakawa and Peter Fiebig PDF

Trans. Amer. Math. Soc. 364 (2012), 4683-4712 Request permission

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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