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Geometric construction of highest weight crystals for quantum generalized Kac–Moody algebras

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Abstract

We present a geometric construction of highest weight crystals B(λ) for quantum generalized Kac–Moody algebras. It is given in terms of the irreducible components of certain Lagrangian subvarieties of Nakajima’s quiver varieties associated to quivers with edge loops.

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Authors and Affiliations

  1. Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University, 599 Gwanak-Ro, Gwanak-Gu, Seoul, 151-747, Korea

    Seok-Jin Kang

  2. Research Institute for Mathematical Sciences, Kyoto University, Kitashirakawa, Sakyo-Ku, Kyoto, 606-8502, Japan

    Masaki Kashiwara

  3. Département de Mathématiques, Université Pierre et Marie Curie, 175 rue du Chevaleret, 75013, Paris, France

    Olivier Schiffmann

Authors
  1. Seok-Jin Kang
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  2. Masaki Kashiwara
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  3. Olivier Schiffmann
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Corresponding author

Correspondence to Seok-Jin Kang.

Additional information

S.-J. Kang research was supported by KRF Grant # 2007-341-C00001.

M. Kashiwara research was partially supported by Grant-in-Aid for Scientific Research (B) 18340007, Japan Society for the Promotion of Science.

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Kang, SJ., Kashiwara, M. & Schiffmann, O. Geometric construction of highest weight crystals for quantum generalized Kac–Moody algebras. Math. Ann. 354, 193–208 (2012). https://doi.org/10.1007/s00208-011-0725-5

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  • DOI: https://doi.org/10.1007/s00208-011-0725-5

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