On bases of centres of Iwahori-Hecke algebras of the symmetric group

JOURNAL OF ALGEBRA

卷:289

Article

Francis, A ; Jones, L

关键词: Hecke algebra;    center;    minimal basis;    norm;   

DOI  :  10.1016/j.jalgebra.2005.03.030

来源: Elsevier

【 摘 要 】

In 1990, using norms, the second author constructed a basis for the centre of the Hecke algebra of the symmetric group S-n over Q[zeta] [Trans. Amer. Math. Soc. 317 (1) (1990) 361-392]. An integral minimal basis was later given by the first author in [J. Algebra 221 (1) (1999) 1-28], following [M. Geck, R. Rouquier, Centers and simple modules for Iwahori-Hecke algebras, in: Finite Reductive Groups, Luminy, 1994, Birkhauser, Boston, MA, 1997, pp. 251-272]. In principle one can then write elements of the norm basis as integral linear combinations of minimal basis elements. In this paper we find an explicit non-recursive expression for the coefficients appearing in these linear combinations. These coefficients are expressed in terms of certain permutation characters of S-n. In the process of establishing this main theorem, we prove the following items of independent interest: a result on the projection of the norms onto parabolic subalgebras, the existence of an inner product on the Hecke algebra with some interesting properties, and the existence of a partial ordering on the norms. (c) 2005 Elsevier Inc. All rights reserved.

【 授权许可】

Free