منابع مشابه
Monoid Hecke Algebras
This paper concerns the monoid Hecke algebras H introduced by Louis Solomon. We determine explicitly the unities of the orbit algebras associated with the two-sided action of the Weyl group W . We use this to: 1. find a description of the irreducible representations of H, 2. find an explicit isomorphism between H and the monoid algebra of the Renner monoid R, 3. extend the Kazhdan-Lusztig invol...
متن کاملq-rook monoid algebras, Hecke algebras, and Schur-Weyl duality
When we were at the beginnings of our careers Sergei’s support helped us to believe in our work. He generously encouraged us to publish our results on Brauer and Birman-Murakami-Wenzl algebras, results which had in part, or possibly in total, been obtained earlier by Sergei himself. He remains a great inspiration for us, both mathematically and in our memory of his kindness, modesty, generosity...
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 کاملHecke 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 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...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1997
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-97-01823-0