共查询到20条相似文献,搜索用时 553 毫秒
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Laura Geatti 《Differential Geometry and its Applications》2012,30(2):195-205
We consider the action of a real semisimple Lie group G on the complexification of a semisimple symmetric space and we present a refinement of Matsuki?s results (Matsuki, 1997 [1]) in this case. We exhibit a finite set of points in , sitting on closed G-orbits of locally minimal dimension, whose slice representation determines the G-orbit structure of . Every such point lies on a compact torus and occurs at specific values of the restricted roots of the symmetric pair . The slice representation at is equivalent to the isotropy representation of a real reductive symmetric space, namely . In principle, this gives the possibility to explicitly parametrize all G-orbits in . 相似文献
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In this paper we determine the projective unitary representations of finite dimensional Lie supergroups whose underlying Lie superalgebra is , where is a compact simple Lie superalgebra and A is a supercommutative associative (super)algebra; the crucial case is when is a Graßmann algebra. Since we are interested in projective representations, the first step consists in determining the cocycles defining the corresponding central extensions. Our second main result asserts that, if is a simple compact Lie superalgebra with , then each (projective) unitary representation of factors through a (projective) unitary representation of itself, and these are known by Jakobsen's classification. If , then we likewise reduce the classification problem to semidirect products of compact Lie groups K with a Clifford–Lie supergroup which has been studied by Carmeli, Cassinelli, Toigo and Varadarajan. 相似文献
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Dave Anderson Mathieu Florence Zinovy Reichstein 《Comptes Rendus Mathematique》2013,351(23-24):871-875
Let G be a split simple group of type over a field k, and let be its Lie algebra. Answering a question of J.-L. Colliot-Thélène, B. Kunyavski?, V.L. Popov, and Z. Reichstein, we show that the function field is generated by algebraically independent elements over the field of adjoint invariants . 相似文献
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Let G be a complex linear algebraic group, its Lie algebra and a nilpotent element. Vust's Theorem says that in case of , the algebra , where is the stabilizer of e under the adjoint action, is generated by the image of the natural action of d-th symmetric group and the linear maps . In this paper, we give an analogue of Vust's Theorem for and when the nilpotent elements e satisfy that is normal. As an application, we study the higher Schur–Weyl duality in the sense of [4] for types B, C and D, which establishes a relationship between W-algebras and degenerate affine braid algebras. 相似文献
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Katsunori Kawamura 《Linear algebra and its applications》2012,436(7):2638-2652
Let denote the -algebra defined as the direct sum of all matrix algebras . It is known that has a non-cocommutative comultiplication . From a certain set of transformations of integers, we construct a universal R-matrix R of the -bialgebra such that the quasi-cocommutative -bialgebra is triangular. Furthermore, it is shown that certain linear Diophantine equations are corresponded to the Yang–Baxter equations of R. 相似文献
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With any -manifold M are associated two dglas and , whose cohomologies and are Gerstenhaber algebras. We establish a formality theorem for -manifolds: there exists an quasi-isomorphism whose first ‘Taylor coefficient’ (1) is equal to the Hochschild–Kostant–Rosenberg map twisted by the square root of the Todd cocycle of the -manifold M, and (2) induces an isomorphism of Gerstenhaber algebras on the level of cohomology. Consequently, the Hochschild–Kostant–Rosenberg map twisted by the square root of the Todd class of the -manifold M is an isomorphism of Gerstenhaber algebras from to . 相似文献
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Pham Hung Quy 《Journal of Pure and Applied Algebra》2018,222(5):1126-1138
Let be an equidimensional excellent local ring of characteristic . The aim of this paper is to show that does not depend on the choice of parameter ideal provided R is an F-injective local ring that is F-rational on the punctured spectrum. 相似文献
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Let be a bounded domain satisfying a Hayman-type asymmetry condition, and let D be an arbitrary bounded domain referred to as an “obstacle”. We are interested in the behavior of the first Dirichlet eigenvalue .First, we prove an upper bound on in terms of the distance of the set to the set of maximum points of the first Dirichlet ground state of Ω. In short, a direct corollary is that if
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is large enough in terms of , then all maximizer sets of are close to each maximum point of .Second, we discuss the distribution of and the possibility to inscribe wavelength balls at a given point in Ω.Finally, we specify our observations to convex obstacles D and show that if is sufficiently large with respect to , then all maximizers of contain all maximum points of . 相似文献