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Some remarkable degenerations of quantum groups

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Abstract

We show that an irreducible representation of a quantized enveloping algebraU ε at a ℓth root of 1 has maximal dimension (=ℓN) if the corresponding symplectic leaf has maximal dimension (=2N). The method of the proof consists of a construction of a sequence of degenerations ofU ε, the last one being aq-commutative algebraU (2N)ε . This allows us to reduce many problems concerningU ε to that concerningU (2N)ε .

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Authors and Affiliations

  1. Scuola Normale Superiore, Pisa, Italy

    C. De Concini

  2. Department of Mathematics, MIT, 02139, Cambridge, MA, USA

    V. G. Kac

  3. Dipartimento di Matematica, Universit degli studi di Roma “La Sapienza”, Rome, Italy

    C. Procesi

Authors
  1. C. De Concini
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  2. V. G. Kac
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  3. C. Procesi
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Communicated by A. Jaffe

To Armand Borel on his 70th birthday

Supported in part by the NSF grant DMS-9103792

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De Concini, C., Kac, V.G. & Procesi, C. Some remarkable degenerations of quantum groups. Commun.Math. Phys. 157, 405–427 (1993). https://doi.org/10.1007/BF02099768

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  • DOI: https://doi.org/10.1007/BF02099768

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