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86
Modules for Algebraic Groups With Finitely Many Orbits on Subspaces
, 1997
"... Introduction Let G be a connected linear algebraic group over an algebraically closed field K of characteristic p 0. In this paper we determine all finitedimensional irreducible rational KGmodules V such that G has only a finite number of orbits on the set of vectors in V . We shall call such a ..."
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Cited by 13 (5 self)
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Introduction Let G be a connected linear algebraic group over an algebraically closed field K of characteristic p 0. In this paper we determine all finitedimensional irreducible rational KGmodules V such that G has only a finite number of orbits on the set of vectors in V . We shall call such a
Finite dimensional representations of rational Cherednik algebras
"... A complete classification and character formulas for finitedimensional irreducible representations of the rational Cherednik algebra of type A are given. Less complete results for other types are obtained. Links to the geometry of affine flag manifolds and Hilbert schemes are discussed. 1 Main resu ..."
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Cited by 37 (1 self)
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A complete classification and character formulas for finitedimensional irreducible representations of the rational Cherednik algebra of type A are given. Less complete results for other types are obtained. Links to the geometry of affine flag manifolds and Hilbert schemes are discussed. 1 Main
Finite dimensional modules for rational Cherednik algebras
, 2006
"... We construct and study some finite dimensional modules for rational Cherednik algebras for the groups G(r, p, n) by using intertwining operators and a commutative family of operators introduced by Dunkl and Opdam. The coinvariant ring and an analog of the ring constructed by Gordon in the course of ..."
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Cited by 5 (3 self)
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We construct and study some finite dimensional modules for rational Cherednik algebras for the groups G(r, p, n) by using intertwining operators and a commutative family of operators introduced by Dunkl and Opdam. The coinvariant ring and an analog of the ring constructed by Gordon in the course
Finite dimensional representations of the rational Cherednik algebra for G4
 J. of Algebra
"... Abstract. In this paper, we study representations of the rational Cherednik algebra associated to the complex reflection group G4. In particular, we classify the irreducible finite dimensional representations and compute their characters. 1. ..."
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Abstract. In this paper, we study representations of the rational Cherednik algebra associated to the complex reflection group G4. In particular, we classify the irreducible finite dimensional representations and compute their characters. 1.
COHOMOLOGY OF FINITE GROUP SCHEMES OVER A FIELD
"... A finite group scheme G over a field k is equivalent to its coordinate algebra, a finite dimensional commutative Hopf algebra k[G] over k. In many contexts, it is natural to consider the rational (or Hochschild) cohomology of G with coefficients in a k[G]comodule M. This is naturally isomorphic to ..."
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Cited by 111 (14 self)
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A finite group scheme G over a field k is equivalent to its coordinate algebra, a finite dimensional commutative Hopf algebra k[G] over k. In many contexts, it is natural to consider the rational (or Hochschild) cohomology of G with coefficients in a k[G]comodule M. This is naturally isomorphic
Rational Cherednik algebras and Hilbert schemes
"... Abstract. Let Hc be the rational Cherednik algebra of type An−1 with spherical subalgebra Uc = eHce. Then Uc is filtered by order of differential operators with associated graded ring gr Uc = C[h ⊕ h ∗ ] W, where W is the nth symmetric group. Using the Zalgebra construction from [GS] it is also po ..."
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Cited by 58 (6 self)
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, so that Lc(triv) is the unique onedimensional simple Hcmodule, then Φ(eLc(triv)) ∼ = OZn, where Zn = τ −1 (0) is the punctual Hilbert scheme. • If c = 1/n + k for k ∈ N then, under a canonical filtration on the finite dimensional module Lc(triv), gr eLc(triv) has a natural bigraded structure
Geometric rationality of Satake compactifications
"... Throughout this paper, except in a few places, let G = the Rrational points on a reductive group defined over R K = a maximal compact subgroup X = the associated symmetric space Let (π, V) be a finitedimensional algebraic representation of G. Eventually G will be assumed semisimple and π irreduci ..."
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Cited by 2 (0 self)
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Throughout this paper, except in a few places, let G = the Rrational points on a reductive group defined over R K = a maximal compact subgroup X = the associated symmetric space Let (π, V) be a finitedimensional algebraic representation of G. Eventually G will be assumed semisimple and π
Double of the Yangian and rational Rmatrices
"... Studying the algebraic structure of the double DY (g) of the yangian Y (g) we present the triangular decomposition of DY (g) and a factorization for the canonical pairing of the yangian with its dual inside DY (g). As a consequence we obtain an explicit formula for the universal Rmatrix of DY (g) a ..."
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of finitedimensional representations of yangians produce rational solutions of the YangBax...
Geometric representations of graded and rational Cherednik algebras of type An
 In preparation
"... Abstract. We provide geometric constructions of modules over the graded Cherednik algebra Hgrν and the rational Cherednik algebra H rat ν attached to a simple algebraic group G together with a pinned automorphism θ. These modules are realized on the cohomology of affine Springer fibers (of finite ty ..."
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Cited by 3 (0 self)
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the irreducible finitedimensional spherical modules Lν(triv) of H gr ν and of Hratν. We give a formula for the dimension of Lν(triv) and give a geometric interpretation of its
RATIONAL RECIPROCITY LAWS
"... The purpose of this note is to provide an overview of Rational Reciprocity (and in particular, of Scholz’s reciprocity law) for the nonnumber theorist. In the first part, we will describe the background in number theory that will be necessary for a complete understanding of the material to be discu ..."
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the remainder of this note. By an algebraic number field K, we mean a finite dimensional extension of Q. If K and L are two algebraic number fields satisfying K ⊆ L, then L can be viewed as a Kvector space and we denote its dimension by [L: K]. By the Primitive Element Theorem, there exists a ∈ L such that L
Results 1  10
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86