The Segal-Bargmann "Coherent State" Transform for Compact Lie Groups
نویسندگان
چکیده
منابع مشابه
Geometric Quantization and the Generalized Segal–Bargmann Transform for Lie Groups of Compact Type
Let K be a connected Lie group of compact type and let T ∗(K) be its cotangent bundle. This paper considers geometric quantization of T ∗(K), first using the vertical polarization and then using a natural Kähler polarization obtained by identifying T ∗(K) with the complexified group KC. The first main result is that the Hilbert space obtained by using the Kähler polarization is naturally identi...
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Abstract. Let G be a connected complex semisimple group, assumed to have trivial center, and let K be a maximal compact subgroup of G. Then G/K, with a fixed G-invariant Riemannian metric, is a Riemannian symmetric space of the complex type. Now let Γ be a discrete subgroup of G that acts freely and cocompactly on G/K. We consider the Segal–Bargmann transform, defined in terms of the heat equat...
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Analysis of function spaces and special functions are closely related to the representation theory of Lie groups. We explain here the connection between the Laguerre functions, the Laguerre polynomials, and the Meixner-Pollacyck polynomials on the one side, and highest weight representations of Hermitian Lie groups on the other side. The representation theory is used to derive differential equa...
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ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 1994
ISSN: 0022-1236
DOI: 10.1006/jfan.1994.1064