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CELLULAR ALGEBRAS AND CENTERS OF HECKE ALGEBRAS

  • Jeong, Yeon-Kwan (Department of Mathematics, Seoul National University) ;
  • Lee, In-Sok (Department of Mathematics, Seoul National University) ;
  • Oh, Hyekyung (Department of Mathematics, Seoul National University) ;
  • Park, Kyung-Hwan (Department of Mathematics, Seoul National University)
  • Published : 2002.02.01

Abstract

In this short note, we find bases of the centers of generic Hecke algebras associated with certain finite Coxeter groups. Our bases are described using the notion of cell datum of Graham and Lehrer, and the notion of norm.

References

  1. Reflection groups and Coxeter groups J. E. Humphreys
  2. Invent. Math. v.53 Representations of Coxeter groups and Hecke algebras D. Kazhdan;G. Lusztig https://doi.org/10.1007/BF01390031
  3. Proc. London Math. Soc. v.70 no.3 Hecke algebras of type $B_n$ at roots of unity R. Dipper;G. D. James;G. E. Murphy https://doi.org/10.1112/plms/s3-70.3.505
  4. J. Algebra v.173 The representations of Hecke algebras of type $A_n$ G. E. Murphy https://doi.org/10.1006/jabr.1995.1079
  5. J. Algebra v.126 The Lusztig isomorphism for Hecke algebras of dihedral type A. P. Fakiolas https://doi.org/10.1016/0021-8693(89)90314-1
  6. J. Algebra v.71 On a theorem of Benson and Curtis G. Lusztig https://doi.org/10.1016/0021-8693(81)90188-5
  7. Invent. Math. v.123 Cellular algebras J. J. Graham;G. I. Lehrer https://doi.org/10.1007/BF01232365
  8. Progr. Math. v.141 Centers and simple modules for Iwahori-Hecke algebras M. Geck;R. Rouquier
  9. Trans. Amer. Math. Soc. v.317 Centers of generic Hecke algebras L. K. Jones https://doi.org/10.2307/2001467
  10. The symmetric group: Representations, combinatorial algorithms symmetric functions B. E. Sagan
  11. Cellular Bases of Hecke algebras of type $D_2k+1$ Y.-K. Jeong;I.-S. Lee;H. Oh; K.-H. Park

Cited by

  1. Standardly based algebras and 0-Hecke algebras vol.14, pp.10, 2015, https://doi.org/10.1142/S0219498815501418
  2. CENTRES OF SYMMETRIC CELLULAR ALGEBRAS vol.82, pp.03, 2010, https://doi.org/10.1017/S0004972710001620
  3. Hecke algebras of finite type are cellular vol.169, pp.3, 2007, https://doi.org/10.1007/s00222-007-0053-2