Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

The noncommutativity of Hecke algebras associated to Weyl groups


Author: Michael R. Anderson
Journal: Proc. Amer. Math. Soc. 123 (1995), 2363-2368
MSC: Primary 20F55; Secondary 16S99, 20C33
MathSciNet review: 1254829
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Abstract: We prove that the Hecke algebra $ \mathcal{H}(W,{W_J})$, where W is a Weyl group of spherical type and $ {W_J}$ is a standard parabolic subgroup of W of corank $ \geq 2$, is noncommutative.


References [Enhancements On Off] (What's this?)

  • [A] M. R. Anderson, Hecke algebras associated to Weyl groups, Ph.D. thesis, Ohio State University, 1993.
  • [BC] W. Bosma and J. Cannon, Handbook of Cayley functions, Sydney, 1992.
  • [BCN] A. E. Brouwer, A. M. Cohen, and A. Neumaier, Distance-regular graphs, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 18, Springer-Verlag, Berlin, 1989. MR 1002568
  • [CIK] C. W. Curtis, N. Iwahori, and R. Kilmoyer, Hecke algebras and characters of parabolic type of finite groups with (𝐵, 𝑁)-pairs, Inst. Hautes Études Sci. Publ. Math. 40 (1971), 81–116. MR 0347996
  • [Hu] James E. Humphreys, Introduction to Lie algebras and representation theory, Springer-Verlag, New York-Berlin, 1972. Graduate Texts in Mathematics, Vol. 9. MR 0323842
  • [I] N. Iwahori, On some properties of groups with BN-pairs, Theory of Finite Groups (Brauer and Sah, eds.), Benjamin, New York, 1969.
  • [K] Aloys Krieg, Hecke algebras, Mem. Amer. Math. Soc. 87 (1990), no. 435, x+158. MR 1027069, 10.1090/memo/0435
  • [Su] Michio Suzuki, Group theory. I, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 247, Springer-Verlag, Berlin-New York, 1982. Translated from the Japanese by the author. MR 648772
  • [T] Jacques Tits, Buildings of spherical type and finite BN-pairs, Lecture Notes in Mathematics, Vol. 386, Springer-Verlag, Berlin-New York, 1974. MR 0470099

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1995-1254829-9
Article copyright: © Copyright 1995 American Mathematical Society