A Holomorphic Representation of the Multidimensional Jacobi Algebra
نویسنده
چکیده
A holomorphic representation of the Jacobi algebra hn⋊sp(n,R) by first order differential operators with polynomial coefficients on the manifold C × Dn is presented. The Hilbert space of holomorphic functions on which the holomorphic first order differential operators with polynomials coefficients act is constructed.
منابع مشابه
A Holomorphic Representation of the Jacobi Algebra
A representation of the Jacobi algebra h1 ⋊ su(1, 1) by first order differential operators with polynomial coefficients on the manifold C×D1 is presented. The Hilbert space of holomorphic functions on which the holomorphic first order differential operators with polynomials coefficients act is constructed.
متن کاملBilinear Summation Formulas from Quantum Algebra Representations
The tensor product of a positive and a negative discrete series representation of the quantum algebra Uq ( su(1, 1) ) decomposes as a direct integral over the principal unitary series representations. Discrete terms can appear, and these terms are a finite number of discrete series representations, or one complementary series representation. From the interpretation as overlap coefficients of li...
متن کاملRozansky-witten Invariants via Atiyah Classes
Recently, L.Rozansky and E.Witten [RW] associated to any hyper-Kähler manifold X an invariant of topological 3-manifolds. In fact, their construction gives a system of weights c Γ (X) associated to 3-valent graphs Γ and the corresponding invariant of a 3-manifold Y is obtained as the sum c Γ (X)I Γ (Y) where I Γ (Y) is the standard integral of the product of linking forms. So the new ingredient...
متن کاملInvariants via Atiyah Classes
Recently, L.Rozansky and E.Witten [RW] associated to any hyper-Kähler manifold X an invariant of topological 3-manifolds. In fact, their construction gives a system of weights c Γ (X) associated to 3-valent graphs Γ and the corresponding invariant of a 3-manifold Y is obtained as the sum c Γ (X)I Γ (Y) where I Γ (Y) is the standard integral of the product of linking forms. So the new ingredient...
متن کاملIsomorphisms of the Jacobi and Poisson Brackets
We present a general theorem describing the isomorphisms of the local Lie algebra structures on the spaces of smooth (real-analytic or holomorphic) functions on smooth (resp. real-analytic, Stein) manifolds, as for example those given by Poisson or contact structures, but we consider degenerate structures as well. Introduction We shall admit different classes of smoothness, so by a manifold of ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2006