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19
Weakly grouptheoretical and solvable fusion categories
"... To Izrail Moiseevich Gelfand on his 95th birthday with admiration ..."
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Cited by 59 (8 self)
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To Izrail Moiseevich Gelfand on his 95th birthday with admiration
Invariant ∗products on coadjoint orbits and the Shapovalov pairing
, 2003
"... We give an explicit formula for invariant ∗products on a wide class of coadjoint orbits. The answer is expressed in terms of the Shapovalov pairing for generalized Verma modules. ..."
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We give an explicit formula for invariant ∗products on a wide class of coadjoint orbits. The answer is expressed in terms of the Shapovalov pairing for generalized Verma modules.
QUANTIZATION OF CLASSICAL DYNAMICAL rMATRICES WITH Nonabelian Base
, 2003
"... . We construct some classes of dynamical rmatrices over a nonabelian base, and quantize some of them by constructing dynamical (pseudo)twists in the sense of Xu. This way, we obtain quantizations of rmatrices obtained in earlier work of the second author with Schiffmann and Varchenko. A part of o ..."
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. We construct some classes of dynamical rmatrices over a nonabelian base, and quantize some of them by constructing dynamical (pseudo)twists in the sense of Xu. This way, we obtain quantizations of rmatrices obtained in earlier work of the second author with Schiffmann and Varchenko. A part of our construction may be viewed as a generalization of the DoninMudrov nonabelian fusion construction. We apply these results to the construction of equivariant starproducts on Poisson homogeneous spaces, which include some homogeneous spaces introduced by De Concini.
QUANTIZATION OF SOME POISSONLIE DYNAMICAL rMATRICES AND POISSON HOMOGENEOUS SPACES
, 2004
"... Abstract. PoissonLie (PL) dynamical rmatrices are generalizations of dynamical rmatrices, where the base is a PoissonLie group. We prove analogues of basic results for these rmatrices, namely constructions of (quasi)Poisson groupoids and of Poisson homogeneous spaces. We introduce a class of PL ..."
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Abstract. PoissonLie (PL) dynamical rmatrices are generalizations of dynamical rmatrices, where the base is a PoissonLie group. We prove analogues of basic results for these rmatrices, namely constructions of (quasi)Poisson groupoids and of Poisson homogeneous spaces. We introduce a class of PL dynamical rmatrices, associated to nondegenerate Lie bialgebras with a splitting; this is a generalization of trigonometric rmatrices with an abelian base. We prove a composition theorem for PL dynamical rmatrices, and construct quantizations of the polarized PL dynamical rmatrices. This way, we obtain quantizations of Poisson homogeneous structures on G/L (G a semisimple Lie group, L a Levi subgroup), thereby generalizing earlier constructions.
Quantum conjugacy classes of simple matrix groups
 Commun. Math. Phys
"... Abstract Let G be a simple complex classical group and g its Lie algebra. Let U (g) be the DrinfeldJimbo quantization of the universal enveloping algebra U(g). We construct an explicit U (g)equivariant quantization of conjugacy classes of G with Levi subgroups as the stabilizers. ..."
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Abstract Let G be a simple complex classical group and g its Lie algebra. Let U (g) be the DrinfeldJimbo quantization of the universal enveloping algebra U(g). We construct an explicit U (g)equivariant quantization of conjugacy classes of G with Levi subgroups as the stabilizers.
Tarasov: Dynamical YangBaxter equations, quasiPoisson homogeneous spaces, and quantization
"... This paper is a continuation of [10]. Let us recall the main result of [10]. Let G be a Lie group, g = Lie G, U ⊂ G a connected closed Lie subgroup such that the corresponding subalgebra u ⊂ g is reductive in g (i.e., there exists an ..."
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This paper is a continuation of [10]. Let us recall the main result of [10]. Let G be a Lie group, g = Lie G, U ⊂ G a connected closed Lie subgroup such that the corresponding subalgebra u ⊂ g is reductive in g (i.e., there exists an
Dynamical reflection equation
"... We construct a dynamical reflection equation algebra, ˜ K, via a dynamical twist of the ordinary reflection equation algebra. A dynamical version of the reflection equation is deduced as a corollary. We show that ˜ K is a right comodule algebra over a dynamical analog of the FaddeevReshetikhinTak ..."
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We construct a dynamical reflection equation algebra, ˜ K, via a dynamical twist of the ordinary reflection equation algebra. A dynamical version of the reflection equation is deduced as a corollary. We show that ˜ K is a right comodule algebra over a dynamical analog of the FaddeevReshetikhinTakhtajan algebra equipped with a structure of right bialgebroid. We introduce dynamical trace and use it for constructing central elements of ˜ K.
Irreducible highestweight modules and equivariant quantization
, 2005
"... The notion of deformation quantization, motivated by ideas coming from both physics and mathematics, was introduced in classical papers [2, 7, 8]. Roughly speaking, a deformation quantization of a Poisson manifold (P, { ,}) is a formal ..."
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The notion of deformation quantization, motivated by ideas coming from both physics and mathematics, was introduced in classical papers [2, 7, 8]. Roughly speaking, a deformation quantization of a Poisson manifold (P, { ,}) is a formal
PoissonLie dynamical rmatrices from Dirac reduction
, 2004
"... The Dirac reduction technique used previously to obtain solutions of the classical dynamical YangBaxter equation on the dual of a Lie algebra is extended to the PoissonLie case and is shown to yield naturally certain dynamical rmatrices on the duals of PoissonLie groups found by Etingof, Enrique ..."
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The Dirac reduction technique used previously to obtain solutions of the classical dynamical YangBaxter equation on the dual of a Lie algebra is extended to the PoissonLie case and is shown to yield naturally certain dynamical rmatrices on the duals of PoissonLie groups found by Etingof, Enriquez and Marshall in math.QA/0403283.