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Runner Removal Morita Equivalences

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Representation Theory of Algebraic Groups and Quantum Groups

Part of the book series: Progress in Mathematics ((PM,volume 284))

Abstract

Let \({U}_{q} = {U}_{q}({\mathfrak{g}\mathfrak{l}}_{n})\) be Lusztig’s divided power quantum general linear group over the complex field with parameter q, a root of unity. We investigate the category of finite-dimensional modules over U q . Lusztig’s famous character formula for simple modules over U q is written purely in terms of the affine Weyl group and its Hecke algebra, which are independent ofq. Our result may be viewed as the categorical version of this independence. Moreover, our methods are valid over fields of positive characteristic. The proof uses the modular representation theory of symmetric groups and finite general linear groups, and the notions of sl2-categorification and perverse equivalences.

Mathematics Subject Classifications (2000): 16D90, 18E30, 20G42, 20G43, 20G05, 20G40, 20C08, 33D80

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Bristol, University Walk, Bristol, BS8 1TW, UK

    Hyohe Miyachi

  2. Graduate School of Mathematics, Nagoya University, Chikusa-ku, Nagoya Aichi, Japan

    Hyohe Miyachi

Authors
  1. Joseph Chuang
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  2. Hyohe Miyachi
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Corresponding author

Correspondence to Hyohe Miyachi .

Editor information

Editors and Affiliations

  1. Graduate School of Mathematics, Nagoya University, Nagoya, 464-8602, Japan

    Akihiko Gyoja

  2. Research Institute for Mathematical Scie, Kyoto University, Kyoto, 606-8502, Japan

    Hiraku Nakajima

  3. Faculty of Science and Technology, Sophia University, Department of Information and Communication Sciences -1, Tokyo, 102-8554, Japan

    Ken-ichi Shinoda

  4. Graduate School of Mathematics, Nagoya University, Nagoya, 464-8602, Japan

    Toshiaki Shoji

  5. Graduate School of Science, Osaka City University, Department of Mathematics -3-138, Osaka, 558-8585, Japan

    Toshiyuki Tanisaki

Additional information

Dedicated to Ken-ichi Shinoda and Toshiaki Shoji on the occasions of their 60th birthdays.

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Chuang, J., Miyachi, H. (2010). Runner Removal Morita Equivalences. In: Gyoja, A., Nakajima, H., Shinoda, Ki., Shoji, T., Tanisaki, T. (eds) Representation Theory of Algebraic Groups and Quantum Groups. Progress in Mathematics, vol 284. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4697-4_4

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