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147,579
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
The generalized Terwilliger algebra and its finitedimensional modules when d = 2
 J. Algebra
"... In [39] Terwilliger considered the Calgebra generated by a given Bose Mesner algebra M and the associated dual Bose Mesner algebra M∗. This algebra is now known as the Terwilliger algebra and is usually denoted by T. Terwilliger showed that each vanishing intersection number and Krein parameter of ..."
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Cited by 1 (0 self)
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relations. T is infinitedimensional and noncommutative in general. In this paper we study T and its finitedimensional modules when d = 2 and T has no “extra ” vanishing intersection numbers or dual intersection numbers. In this case we show T is Calgebra isomorphic to M3(C) ⊕ A, where M3(C) denotes
DEFORMATION THEORY OF FINITE DIMENSIONAL MODULES AND ALGEBRAS
"... Many mathematical structures can be deformed: • Manifolds with possibly an extra (e.g. Poisson) structure • Abelian or triangulated categories • Lie algebras and their universal enveloping algebras ..."
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Cited by 2 (0 self)
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Many mathematical structures can be deformed: • Manifolds with possibly an extra (e.g. Poisson) structure • Abelian or triangulated categories • Lie algebras and their universal enveloping algebras
CLASSIFICATION OF FINITE DIMENSIONAL MODULES OF SINGLY ATYPICAL TYPE OVER THE LIE SUPERALGEBRAS sl(m/n)
, 1999
"... ABSTRACT. We classify the finite dimensional indecomposable sl(m/n)modules with at least a typical or singly atypical primitive weight. We do this classification not only for weight modules, but also for generalized weight modules. We obtain that such a generalized weight module is simply a module ..."
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ABSTRACT. We classify the finite dimensional indecomposable sl(m/n)modules with at least a typical or singly atypical primitive weight. We do this classification not only for weight modules, but also for generalized weight modules. We obtain that such a generalized weight module is simply a module
Solutions of the qKZB equations in tensor products of finite dimensional modules over the elliptic quantum group Eτ,ηsl2
 FIELDS INST. COMMUN
, 1997
"... We consider the quantized KnizhnikZamolodchikovBernarddifference equation (qKZB) with step p and values in a tensor product of finite dimensional evaluation modules over the elliptic quantum group Eτ,η(sl2), the equation defined in terms of elliptic dynamical Rmatrices. We solve the equation in ..."
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Cited by 5 (4 self)
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We consider the quantized KnizhnikZamolodchikovBernarddifference equation (qKZB) with step p and values in a tensor product of finite dimensional evaluation modules over the elliptic quantum group Eτ,η(sl2), the equation defined in terms of elliptic dynamical Rmatrices. We solve the equation
ON MODULE CATEGORIES OVER FINITEDIMENSIONAL HOPF ALGEBRAS
, 2006
"... Abstract. We show that indecomposable exact module categories over the category RepH of representations of a finitedimensional Hopf algebra H are classified by left comodule algebras, Hsimple from the right and with trivial coinvariants, up to equivariant Morita equivalence. Specifically, any inde ..."
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Cited by 18 (4 self)
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Abstract. We show that indecomposable exact module categories over the category RepH of representations of a finitedimensional Hopf algebra H are classified by left comodule algebras, Hsimple from the right and with trivial coinvariants, up to equivariant Morita equivalence. Specifically, any
Verma modules and preprojective algebras
, 2008
"... We give a geometric construction of the Verma modules of a symmetric KacMoody Lie algebra g in terms of constructible functions on the varieties of nilpotent finitedimensional modules of the corresponding preprojective algebra Λ. ..."
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Cited by 12 (4 self)
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We give a geometric construction of the Verma modules of a symmetric KacMoody Lie algebra g in terms of constructible functions on the varieties of nilpotent finitedimensional modules of the corresponding preprojective algebra Λ.
CONVERSE SECOND WHITEHEAD LEMMA
, 704
"... Abstract. We show that finitedimensional Lie algebras over a field of characteristic zero such that the second cohomology group in every finitedimensional module vanishes, are, essentially, semisimple. ..."
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Abstract. We show that finitedimensional Lie algebras over a field of characteristic zero such that the second cohomology group in every finitedimensional module vanishes, are, essentially, semisimple.
A CONVERSE TO THE SECOND WHITEHEAD LEMMA
, 704
"... Abstract. We show that finitedimensional Lie algebras over a field of characteristic zero such that the second cohomology group in every finitedimensional module vanishes, are, essentially, semisimple. ..."
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Abstract. We show that finitedimensional Lie algebras over a field of characteristic zero such that the second cohomology group in every finitedimensional module vanishes, are, essentially, semisimple.
Results 1  10
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147,579