On the restricted Verma modules at the critical level

Abstract

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.

30 pages, revised version

References in corpus (2)

• Lusztig's conjecture as a moment graph problem
• D-modules on the affine flag variety and representations of affine Kac-Moody algebras

Cited by in corpus (2)

• W-algebras at the critical level
• On the restricted projective objects in the affine category O at the critical level