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

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Symmetries, Integrable Systems and Representations

Part of the book series: Springer Proceedings in Mathematics & Statistics ((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.

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References

  1. Arakawa, T., Fiebig, P.: On the restricted Verma modules at the critical level. Trans. Am. Math. Soc. 364(9), 4683–4712 (2012)

    Article  MathSciNet  Google Scholar 

  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. Deodhar, V., Gabber, O., Kac, V.: Structure of some categories of representations of infinite-dimensional Lie algebras. Adv. Math. 45(1), 92–116 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Chapter  Google Scholar 

  5. Kac, V., Kazhdan, D.: Structure of representations with highest weight of infinite-dimensional Lie algebras. Adv. Math. 34, 97–108 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  6. Frenkel, E.: Langlands Correspondence for Loop Groups. Cambridge Studies in Advanced Mathematics, vol. 103. Cambridge University Press, Cambridge (2007)

    MATH  Google Scholar 

  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)

    Chapter  Google Scholar 

  8. Rocha-Caridi, A., Wallach, N.R.: Projective modules over graded Lie algebras. Math. Z. 180, 151–177 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  9. Soergel, W.: Character formulas for tilting modules over Kac–Moody algebras. Represent. Theory 2(13), 432–448 (1998)

    Article  MathSciNet  MATH  Google Scholar 

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Fiebig, P. (2013). On the Subgeneric Restricted Blocks of Affine Category \(\mathcal{O}\) at the Critical Level. In: Iohara, K., Morier-Genoud, S., Rémy, B. (eds) Symmetries, Integrable Systems and Representations. Springer Proceedings in Mathematics & Statistics, vol 40. Springer, London. https://doi.org/10.1007/978-1-4471-4863-0_4

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