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Monoid Hecke algebras 总被引:1,自引:0,他引:1
Mohan S. Putcha 《Transactions of the American Mathematical Society》1997,349(9):3517-3534
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The theory of PBW properties of quadratic algebras, to which this
paper aims to be a modest contribution, originates from the
pioneering work of Drinfeld (see [Dr1]). In particular, as we
learned after publication of [EG] (to the embarrassment of
two of us!), symplectic reflection algebras, as well as PBW theorems for
them, were discovered by Drinfeld in the classical paper [Dr2] 15
years before [EG] (namely, they are a special case of degenerate
affine Hecke algebras for a finite group G introduced in [Dr2, Section
4]). 相似文献
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Ivan Marin 《Comptes Rendus Mathematique》2003,337(5):297-302
In this Note, we define infinitesimal analogues of the Iwahori–Hecke algebras associated with finite Coxeter groups. These are reductive Lie algebras for which we announce several decomposition results. These decompositions yield irreducibility results for representations of the corresponding (pure) generalized braid groups deduced from Hecke algebra representations through tensor constructions. To cite this article: I. Marin, C. R. Acad. Sci. Paris, Ser. I 337 (2003). 相似文献
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Kirsten Bremke 《manuscripta mathematica》1994,83(1):331-346
The purpose of this paper is to calculate the decomposition numbers for Hecke algebras of typeF
4 (andC
3) with unequal parameters. The problem is reduced to specifying decomposition maps of the generic Hecke algebras. The concept
of Kazhdan-Lusztig polynomials and left cells serves to determine their irreducible representations. We also prove a result
about the minimal ring over which the irreducible representations of the generic algebras can be realized. 相似文献
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The Hecke group algebra of a finite Coxeter group , as introduced by the first and last authors, is obtained from by gluing appropriately its 0-Hecke algebra and its group algebra. In this paper, we give an equivalent alternative construction in the case when is the finite Weyl group associated to an affine Weyl group W. Namely, we prove that, for q not a root of unity of small order, is the natural quotient of the affine Hecke algebra H(W)(q) through its level 0 representation.The proof relies on the following core combinatorial result: at level 0 the 0-Hecke algebra H(W)(0) acts transitively on . Equivalently, in type A, a word written on a circle can be both sorted and antisorted by elementary bubble sort operators. We further show that the level 0 representation is a calibrated principal series representation M(t) for a suitable choice of character t, so that the quotient factors (non-trivially) through the principal central specialization. This explains in particular the similarities between the representation theory of the 0-Hecke algebra and that of the affine Hecke algebra H(W)(q) at this specialization. 相似文献
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Let
be the Hecke algebra of the symmetric group
over a field K of characteristic
and
a primitive
-th root of one in K. We show that an
-module is projective if and only if its restrictions to any
-parabolic subalgebra of
is projective.
Moreover, we give a new construction of blocks of
-parabolic subalgebras, in terms of skew group algebras over local commutative
algebras.
Received: 30 June 2003 相似文献
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Marcelo Laca Nadia S. Larsen 《Proceedings of the American Mathematical Society》2003,131(7):2189-2199
We consider group-subgroup pairs in which the group is a semidirect product and the subgroup is contained in the normal part. We give conditions for the pair to be a Hecke pair and we show that the enveloping Hecke algebra and Hecke -algebra are canonically isomorphic to semigroup crossed products, generalizing earlier results of Arledge, Laca and Raeburn and of Brenken.
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Let be the Hecke algebra associated with a Coxeter system (W, R). The structure constants of with respect to various bases are Laurent polynomials, whose coefficients enjoy remarkable positivity properties. We survey these and prove some new ones using the relationship between and the geometry of Schubert varieties.To Professor Jacques Tits on his sixtieth birthday 相似文献
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G. J. Heckman 《Inventiones Mathematicae》1990,100(1):403-417
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R.M. Green 《Mathematische Zeitschrift》1998,229(2):365-383
We study a finite-dimensional quotient of the Hecke algebra of type for general n, using a calculus of diagrams. This provides a basis of monomials in a certain set of generators. Using this, we prove a
conjecture of C.K. Fan about the semisimplicity of the quotient algebra. We also discuss the cellular structure of the algebra,
with certain restrictions on the ground ring.
Received February 24, 1997; in final form May 9, 1997 相似文献
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Eric Opdam 《Advances in Mathematics》2009,220(5):1549-182
In this paper we study homological properties of modules over an affine Hecke algebra H. In particular we prove a comparison result for higher extensions of tempered modules when passing to the Schwartz algebra S, a certain topological completion of the affine Hecke algebra. The proof is self-contained and based on a direct construction of a bounded contraction of certain standard resolutions of H-modules.This construction applies for all positive parameters of the affine Hecke algebra. This is an important feature, since it is an ingredient to analyse how the irreducible discrete series representations of H arise in generic families over the parameter space of H. For irreducible non-simply laced affine Hecke algebras this will enable us to give a complete classification of the discrete series characters, for all positive parameters (we will report on this application in a separate article). 相似文献
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Norihiko Minami 《Transactions of the American Mathematical Society》1999,351(11):4481-4513
In this paper, we define the concept of the cohomotopical Mackey functor, which is more general than the usual cohomological Mackey functor, and show that Hecke algebra techniques are applicable to cohomotopical Mackey functors. Our theory is valid for any (possibly infinite) discrete group. Some applications to topology are also given.
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G. Lusztig 《Selecta Mathematica, New Series》2016,22(4):1953-1986
Let H be a Hecke algebra arising as an endomorphism algebra of the representation of a Chevalley group G over \(F_{q}\) induced by a unipotent cuspidal representation of a Levi quotient L of a parabolic subgroup. We assume that L is not a torus. In this paper we outline a geometric interpretation of the coefficients of the canonical basis of H in terms of perverse sheaves. We illustrate this in detail in the case where the Weyl group of G is ot type \(B_{4}\) and that of L is of type \(B_{2}\). 相似文献
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Anne V. Shepler Sarah Witherspoon 《Transactions of the American Mathematical Society》2008,360(8):3975-4005
We develop and collect techniques for determining Hochschild cohomology of skew group algebras and apply our results to graded Hecke algebras. We discuss the explicit computation of certain types of invariants under centralizer subgroups, focusing on the infinite family of complex reflection groups to illustrate our ideas. Resulting formulas for Hochschild two-cocycles give information about deformations of and, in particular, about graded Hecke algebras. We expand the definition of a graded Hecke algebra to allow a nonfaithful action of on , and we show that there exist nontrivial graded Hecke algebras for , in contrast to the case of the natural reflection representation. We prove that one of these graded Hecke algebras is equivalent to an algebra that has appeared before in a different form.
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