Murphy operators and the centre of the Iwahori – Hecke algebras of type
نویسنده
چکیده
In this paper we introduce a family of polynomials indexed by pairs of partitions and show that if these polynomials are self–orthogonal then the centre of the Iwahori–Hecke algebra of the symmetric group is precisely the set of symmetric polynomials in the Murphy operators.
منابع مشابه
Murphy Operators and the Centre of the Iwahori-Hecke Algebras of Type A
In this paper we introduce a family of polynomials indexed by pairs of partitions and show that if these polynomials are self-orthogonal then the centre of the Iwahori-Hecke algebra of the symmetric group is precisely the set of symmetric polynomials in the Murphy operators.
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This paper presents two results on central elements in Iwahori-Hecke algebras. Both arise from characteristics of the minimal basis for the centre of an IwahoriHecke algebra ([9],[5]). The first, a bauble, is restricted to type A algebras, and describes the elementary symmetric functions of Murphy operators in terms of the minimal basis for the centre. The elementary symmetric functions are of ...
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We use the results on the minimal basis of the centre of an Iwahori-Hecke algebra from our earlier work, as well as some additional results on the minimal basis, to describe the image and kernel of the Brauer homomorphism defined by L. Jones for Iwahori-Hecke algebras of type A.
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