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An inductive approach to representations of complex reflection groups G(m, 1, n)

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Abstract

We propose an inductive approach to the representation theory of the chain of complex reflection groups G(m, 1, n). We obtain the Jucys-Murphy elements of G(m, 1, n) from the Jucys-Murphy elements of the cyclotomic Hecke algebra and study their common spectrum using representations of a degenerate cyclotomic affine Hecke algebra. We construct representations of G(m, 1, n) using a new associative algebra whose underlying vector space is the tensor product of the group ring ℂG(m, 1, n) with a free associative algebra generated by the standard m-tableaux.

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Authors and Affiliations

  1. Centre de Physique Théorique Campus de Luminy, Marseille, France

    O. V. Ogievetsky & L. Poulain d’Andecy

  2. Lebedev Physical Institute, RAS, Moscow, Russia

    O. V. Ogievetsky

Authors
  1. O. V. Ogievetsky
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  2. L. Poulain d’Andecy
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Correspondence to O. V. Ogievetsky.

Additional information

Prepared from an English manuscript submitted by the authors; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 174, No. 1, pp. 109–124, January, 2013.

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Ogievetsky, O.V., Poulain d’Andecy, L. An inductive approach to representations of complex reflection groups G(m, 1, n). Theor Math Phys 174, 95–108 (2013). https://doi.org/10.1007/s11232-013-0008-2

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  • DOI: https://doi.org/10.1007/s11232-013-0008-2

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