The Hecke group algebra of a Coxeter group and its representation theory
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چکیده
منابع مشابه
The Hecke Group Algebra of a Coxeter Group and Its Representation Theory
Let W be a finite Coxeter group. We define its Hecke-group algebra by gluing together appropriately its group algebra and its 0-Hecke algebra. We describe in detail this algebra (dimension, several bases, conjectural presentation, combinatorial construction of simple and indecomposable projective modules, Cartan map) and give several alternative equivalent definitions (as symmetry preserving op...
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We consider a 2-dimensional representation of the Hecke algebra $H(G_7, u)$, where $G_7$ is the complex reflection group and $u$ is the set of indeterminates $u = (x_1,x_2,y_1,y_2,y_3,z_1,z_2,z_3)$. After specializing the indetrminates to non zero complex numbers, we then determine a necessary and sufficient condition that guarantees the irreducibility of the complex specialization of the repre...
متن کاملThe construction of Hecke algebras associated to a Coxeter group
The existence of these Hecke algebras with polynomial coefficients is not quite trivial. There are essentially two constructions in the literature. One originates in Exercices IV.22-25 of [Bourbaki:1968], and is apparently due originally to Jacques Tits. There are other accounts patterned after this argument, for example in [Humphreys:1990] and [Carter:1993]. My reaction to these is that they a...
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The nonstandard Hecke algebra Ȟr was defined in [11] to study the Kronecker problem. We study a quotient Ȟr,2 of Ȟr , called the nonstandard Temperley-Lieb algebra, which is simpler than Ȟr. It is defined to be the subalgebra of Hr,2⊗Hr,2 generated by Pi := C ′ i ⊗C ′ i +Ci ⊗Ci, i ∈ [r− 1], where Hr,2 is the Temperley-Lieb algebra and C i and Ci are Kazhdan-Lusztig basis elements. We give a com...
متن کاملin Algebra . Coxeter groups and Hecke algebras
The finite Coxeter groups are the finite groups generated by reflections on real Euclidean spaces. Examples include dihedral groups, the symmetry groups of regular polytopes (e.g. regular polygons and platonic solids) and the Weyl groups of semisimple complex Lie groups and Lie algebras (such as the special linear group and Lie algebra). General Coxeter groups may be defined as certain (special...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2009
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2008.09.039