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On representations of Hecke algebras

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Abstract

In this report we review some facts about representation theory of Hecke algebras. For Hecke algebras we adapt the approach of A. Okounkov and A. Vershik [Selecta Math., New Ser., 2 (1996) 581], which was developed for the representation theory of symmetric groups. We justify explicit construction of idempotents for Hecke algebras in terms of Jucys-Murphy elements. Ocneanu's traces for these idempotents (which can be interpreted as q-dimensions of corresponding irreducible representations of quantum linear groups) are presented.

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References

  1. V.F.R. Jones: Ann. Math. 126 (1987) 335.

    Article  MATH  Google Scholar 

  2. I.V. Cherednik: Duke Math. J. 54 (1987) 563.

    Article  MathSciNet  MATH  Google Scholar 

  3. G.E. Murphy: J. Algebra 152 (1992) 287. R. Dipper and G. James: Proc. London Math. Soc. 54 (1987) 57.

    Article  MathSciNet  Google Scholar 

  4. H. Wenzl: Invent. Math. 92 (1988) 349.

    Article  MathSciNet  MATH  ADS  Google Scholar 

  5. A. Okounkov and A. Vershik: Selecta Math., New Ser., 2 (1996) 581.

    MathSciNet  MATH  Google Scholar 

  6. A.P. Isaev: Sov. J. Part. Nucl. 28 (1997) 267.

    Google Scholar 

  7. O. Ogievetsky and P. Pyatov: in Proc. of the Int. School. “Symmetries and Integrable Systems”, Dubna, 1999; preprint MPIM (Bonn), MPI 2001-40; http://www.mpim-bonn.mpg.de/html/preprints/preprints.html

  8. M. Jimbo: Lett. Math. Phys. 11 (1986) 247.

    Article  MathSciNet  MATH  ADS  Google Scholar 

  9. L. Faddeev, N. Reshetikhin, and L. Takhtajan: Leningrad Math. J. 1 (1990) 193.

    MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna, Moscow region, 141980, Russia

    A. P. Isaev

  2. Center of Theoretical Physics, Luminy, Marseille, 13288, France

    O. V. Ogievetsky

  3. Theoretical Department, P.N. Lebedev Physical Institute, Leninsky pr. 53, 117924, Moscow, Russia

    O. V. Ogievetsky

Authors
  1. A. P. Isaev
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  2. O. V. Ogievetsky
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Additional information

This work was supported in part by the grants INTAS 03-51-3350 and RFBR 05-01-01086-a.

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Isaev, A.P., Ogievetsky, O.V. On representations of Hecke algebras. Czech J Phys 55, 1433–1441 (2005). https://doi.org/10.1007/s10582-006-0022-9

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  • DOI: https://doi.org/10.1007/s10582-006-0022-9

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