Free probability on Hecke algebras and certain group C^{*}-algebras induced by Hecke algebras
نویسندگان
چکیده
منابع مشابه
Hecke group algebras as degenerate affine Hecke algebras
The Hecke group algebra H W̊ of a finite Coxeter group W̊ , as introduced by the first and last author, is obtained from W̊ by gluing appropriately its 0-Hecke algebra and its group algebra. In this paper, we give an equivalent alternative construction in the case when W̊ is the classical Weyl group associated to an affine Weyl group W . Namely, we prove that, for q not a root of unity, H W̊ is the ...
متن کاملHecke Algebras
which is Artin’s braid relation. In general we will refer to (1) as the braid relation satisfied by si and sj. In order for W to be a Coxeter group it is required that the given set of relations between elements of I give a presentation of W . Informally, this means that any relation between generators in I can be deduced from the fact that the s ∈ Σ have order 2 and the braid relations. Formal...
متن کاملAffine Hecke algebras, cyclotomic Hecke algebras and Clifford theory
We show that the Young tableaux theory and constructions of the irreducible representations of the Weyl groups of type A, B and D, Iwahori-Hecke algebras of types A, B, and D, the complex reflection groups G(r, p, n) and the corresponding cyclotomic Hecke algebras Hr,p,n, can be obtained, in all cases, from the affine Hecke algebra of type A. The Young tableaux theory was extended to affine Hec...
متن کاملAane Hecke Algebras, Cyclotomic Hecke Algebras and Cliiord Theory
We show that the Young tableaux theory and constructions of the irreducible representations of the Weyl groups of type A, can be obtained, in all cases, from the aane Hecke algebra of type A. The Young tableaux theory was extended to aane Hecke algebras (of general Lie type) in recent work of A. Ram. We also show how (in general Lie type) the representations of general aane Hecke algebras can b...
متن کاملSubquotients of Hecke C * -algebras
In [2], Bost and Connes studied a particular Hecke C-algebra CQ arising in number theory. The algebra CQ can be realised as a semigroup crossed product C (Q/Z)⋊αN ∗ by an endomorphic action α of the multiplicative semigroup N on the group Calgebra C(Q/Z) [7], and this realisation has provided useful insight into the analysis of CQ [5, 13]. Since individual elements of Q/Z and N ∗ involve only f...
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ژورنال
عنوان ژورنال: Opuscula Mathematica
سال: 2016
ISSN: 1232-9274
DOI: 10.7494/opmath.2016.36.2.153