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On the Subgeneric Restricted Blocks of Affine Category \(\mathcal{O}\) at the Critical Level

  • Peter Fiebig
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 40)

Abstract

We determine the endomorphism algebra of a projective generator in a subgeneric restricted block of the critical level category \(\mathcal{O}\) over an affine Kac–Moody algebra.

Keywords

Equivalence Class Short Exact Sequence Full Subcategory Verma Module Vertex Algebra 
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References

  1. 1.
    Arakawa, T., Fiebig, P.: On the restricted Verma modules at the critical level. Trans. Am. Math. Soc. 364(9), 4683–4712 (2012) MathSciNetCrossRefGoogle Scholar
  2. 2.
    Arakawa, T., Fiebig, P.: The linkage principle for restricted critical level representations of affine Kac–Moody algebras. Compos. Math. (to appear) Google Scholar
  3. 3.
    Deodhar, V., Gabber, O., Kac, V.: Structure of some categories of representations of infinite-dimensional Lie algebras. Adv. Math. 45(1), 92–116 (1982) MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Fiebig, P.: On the restricted projective objects in the affine category \(\mathcal{O}\) at the critical level. In: Algebraic Groups and Quantum Groups, Nagoya, Japan, 2010. Contemp. Math., vol. 565, pp. 55–70 (2012) CrossRefGoogle Scholar
  5. 5.
    Kac, V., Kazhdan, D.: Structure of representations with highest weight of infinite-dimensional Lie algebras. Adv. Math. 34, 97–108 (1979) MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Frenkel, E.: Langlands Correspondence for Loop Groups. Cambridge Studies in Advanced Mathematics, vol. 103. Cambridge University Press, Cambridge (2007) zbMATHGoogle Scholar
  7. 7.
    Frenkel, E., Gaitsgory, D.: Local geometric Langlands correspondence and affine Kac–Moody algebras. In: Algebraic Geometry and Number Theory. Progr. Math., vol. 253, pp. 69–260. Birkhäuser, Boston (2006) CrossRefGoogle Scholar
  8. 8.
    Rocha-Caridi, A., Wallach, N.R.: Projective modules over graded Lie algebras. Math. Z. 180, 151–177 (1982) MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Soergel, W.: Character formulas for tilting modules over Kac–Moody algebras. Represent. Theory 2(13), 432–448 (1998) MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag London 2013

Authors and Affiliations

  • Peter Fiebig
    • 1
  1. 1.Departement MathematikFAU Erlangen-NürnbergErlangenGermany

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