대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제39권1호
  • /
  • Pages.71-79
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  • 2002
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  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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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)
  • 발행 : 2002.02.01
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초록

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.

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참고문헌

  1. 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
  2. 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
  3. Progr. Math. v.141 Centers and simple modules for Iwahori-Hecke algebras M. Geck;R. Rouquier
  4. Invent. Math. v.123 Cellular algebras J. J. Graham;G. I. Lehrer https://doi.org/10.1007/BF01232365
  5. Reflection groups and Coxeter groups J. E. Humphreys
  6. Cellular Bases of Hecke algebras of type $D_2k+1$ Y.-K. Jeong;I.-S. Lee;H. Oh; K.-H. Park
  7. Trans. Amer. Math. Soc. v.317 Centers of generic Hecke algebras L. K. Jones https://doi.org/10.2307/2001467
  8. Invent. Math. v.53 Representations of Coxeter groups and Hecke algebras D. Kazhdan;G. Lusztig https://doi.org/10.1007/BF01390031
  9. J. Algebra v.71 On a theorem of Benson and Curtis G. Lusztig https://doi.org/10.1016/0021-8693(81)90188-5
  10. J. Algebra v.173 The representations of Hecke algebras of type $A_n$ G. E. Murphy https://doi.org/10.1006/jabr.1995.1079
  11. The symmetric group: Representations, combinatorial algorithms symmetric functions B. E. Sagan

피인용 문헌

  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