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We consider the relationship between the Shapovalov form on an irreducible highest weight module of a semisimple complex Lie algebra, fusion elements, and equivariant quantization. We also discuss some limiting properties of fusion elements.  相似文献   

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Using an equivariant version of Connes? Thom isomorphism, we prove that equivariant K-theory is invariant under strict deformation quantization for a compact Lie group action.  相似文献   

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Reflection equation algebras and related Uq(\mathfrak g){U{_q}(\mathfrak g)} -comodule algebras appear in various constructions of quantum homogeneous spaces and can be obtained via transmutation or equivalently via twisting by a cocycle. In this paper we investigate algebraic and representation theoretic properties of such so called ‘covariantized’ algebras, in particular concerning their centres, invariants, and characters. The locally finite part Fl(Uq (\mathfrak g)){F_l(U{_q} (\mathfrak g))} of Uq(\mathfrak g){U{_q}(\mathfrak g)} with respect to the left adjoint action is a special example of a covariantized algebra. Generalising Noumi’s construction of quantum symmetric pairs we define a coideal subalgebra B f of Uq(\mathfrak g){U{_q}(\mathfrak g)} for each character f of a covariantized algebra. We show that for any character f of Fl(Uq(\mathfrak g)){F_l(U{_q}(\mathfrak g))} the centre Z(B f ) canonically contains the representation ring Rep(\mathfrak g){{\rm Rep}(\mathfrak g)} of the semisimple Lie algebra \mathfrak g{\mathfrak g} . We show moreover that for \mathfrak g = \mathfrak sln(\mathbb C){\mathfrak g = {\mathfrak sl}_n(\mathbb C)} such characters can be constructed from any invertible solution of the reflection equation and hence we obtain many new explicit realisations of Rep(\mathfrak sln(\mathbb C)){{\rm Rep}({\mathfrak sl}_n(\mathbb C))} inside Uq(\mathfrak sln(\mathbb C)){U_q({\mathfrak sl}_n(\mathbb C))} . As an example we discuss the solutions of the reflection equation corresponding to the Grassmannian manifold Gr(m,2m) of m-dimensional subspaces in \mathbb C2m{{\mathbb C}^{2m}}.  相似文献   

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It is shown that a kerneled Langevin equation for the Euclidean model of the sine-Gordon-type field has solutions whose probability distributions converge to a measure. The action functional is not regularized and the space-time dimension is arbitrary. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 115, No. 1, pp. 46–55. April. 1998.  相似文献   

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Let l be an odd prime number and K /k a Galois extension of totally real number fields, with and K /k finite, where k is the cyclotomic -extension of k. The ``main conjecture' of equivariant Iwasawa theory, as formulated in [RW2], is, up to its uniqueness statement, reduced to the existence of a nonabelian pseudomeasure whenever G =G(K /k) is an l-group and Iwasawa's μ-invariant vanishes. This follows from combining the validity of the conjecture in the maximal order case with special congruences. The main tool of proof is a generalization of the Taylor-Oliver integral group logarithm so that it applies to the setting of Iwasawa theory. We acknowledge financial support provided by NSERC and the University of Augsburg.  相似文献   

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Let G be a finite group. For a based G-space X and a Mackey functor M, a topological Mackey functor is constructed, which will be called the stable equivariant abelianization of X with coefficients in M. When X is a based G-CW complex, is shown to be an infinite loop space in the sense of G-spaces. This gives a version of the RO(G)-graded equivariant Dold-Thom theorem. Applying a variant of Elmendorf's construction, we get a model for the Eilenberg-Mac Lane spectrum HM. The proof uses a structure theorem for Mackey functors and our previous results.  相似文献   

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Sedov's variational principle, which is a generalization of the principle of least action to dissipative processes, is used to generalize canonical quantization and the von Neumann equations to dissipative systems. The example of a harmonic oscillator with friction is considered.Institute of Nuclear Physics, State University, Moscow. Translated from Teoreticheskaya i Matematicheskaya Fizika Vol. 100, No. 3, pp. 402–417, September, 1994.  相似文献   

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By using the index theory for unbounded self-adjoint operator equations and the symmetric mountain pass theorem, we investigate the existence of multiple solutions for nonlinear operator equations with twist conditions. We prove an abstract theorem, and give some applications to first order Hamiltonian systems with Sturm–Liouville boundary conditions and delay differential equations.  相似文献   

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In the category of equivariant spaces with base point, we prove the injectivity of the induced map between homotopy sets under some conditions. We study some relations between the localization and the completion. By using these results, we characterize continuous maps which are homotopic on skeletons, and obtain a generalization of the theory of phantom maps.  相似文献   

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Using contact surgery and equivariant bordism theory, we prove the existence of contact structures on all 5-dimensional spin manifolds with certain finite fundamental groups. Received September 13, 1999 / Revised version September 13, 2000 / Published online April 12, 2001  相似文献   

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There has been a popular mistake in equivariant surgery theory for almost a decade. This paper introduces Bak groups, presents their geometric role, and corrects the mistake. The form parameters of A. Bak shed light on the connection of involutions on manifolds to surgery on manifolds.Partially supported by Grant-in-Aid for Scientific Research.Dedicated to Professor Shôrô Araki on his sixtieth birthday  相似文献   

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