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Modules over the small quantum group and semi-infinite flag manifold

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Abstract

We develop a theory of perverse sheaves on the semi-infinite flag manifold G((t))/N((t)) · T[[t]], and show that the subcategory of Iwahori-monodromy perverse sheaves is equivalent to the regular block of the category of representations of the small quantum group at an even root of unity.

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Authors and Affiliations

  1. Department of Mathematics, Yale University, New Haven, CT 06520, USA

    S. Arkhipov

  2. Department of Mathematics, Northwestern University, Evanston, IL 60208, USA

    R. Bezrukavnikov

  3. Department of Mathematics, Brown University, Providence, RI 02912 and Einstein Institute of Mathematics, Edmond J. Safra Campus, Givat Ram, The Hebrew University of Jerusalem, Jerusalem, 91904, Israel

    A. Braverman

  4. Department of Mathematics, University of Chicago, Chicago, IL 60637, USA

    D. Gaitsgory

  5. Department of Mathematics, University of Massachusetts, Amherst, MA 01003, USA

    I. Mirkovic

Authors
  1. S. Arkhipov
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  2. R. Bezrukavnikov
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  3. A. Braverman
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  4. D. Gaitsgory
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  5. I. Mirkovic
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Corresponding authors

Correspondence to S. Arkhipov, R. Bezrukavnikov, A. Braverman, D. Gaitsgory or I. Mirkovic.

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Arkhipov, S., Bezrukavnikov, R., Braverman, A. et al. Modules over the small quantum group and semi-infinite flag manifold. Transformation Groups 10, 279–362 (2005). https://doi.org/10.1007/s00031-005-0401-5

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  • DOI: https://doi.org/10.1007/s00031-005-0401-5

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