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Titlebook: New Developments in Lie Theory and Their Applications; Juan Tirao,Nolan R. Wallach Book 1992 Birkh?user Boston 1992 algebra.lie group.repr

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51#
發(fā)表于 2025-3-30 09:40:54 | 只看該作者
,Some Zeta Functions Attached to ΓG/K,n . of Γ he assigned a certain remarkable analytic function Z.(?, .) (of one complex variable) whose zeros, for example, capture both topological and spectral properties of the space form Γ./. where .= SO(2). Z.(?, .), now called the ., satisfies a functional equation . → 1 → . (involving Harish-Cha
52#
發(fā)表于 2025-3-30 13:29:34 | 只看該作者
53#
發(fā)表于 2025-3-30 19:19:08 | 只看該作者
Unitary Representations of Reductive Lie Groups and the Orbit Method,ge enough to solve a range of interesting harmonic analysis problems. The Kirillov-Kostant philosophy of coadjoint orbits seeks to provide such a family. The purpose of these notes is to describe what is known about implementing that philosophy, particularly for reductive groups.
54#
發(fā)表于 2025-3-30 20:44:16 | 只看該作者
55#
發(fā)表于 2025-3-31 02:21:27 | 只看該作者
56#
發(fā)表于 2025-3-31 05:38:00 | 只看該作者
,The Vanishing of Scalar Curvature on 6 Manifolds, Einstein’s Equation, and Representation Theory,operate on g by the adjoint representation and on g* by the so-called coadjoint representation. Moreover, set .. = .(g). Since the bilinear form (., .) = .(.) on g × g is nonsingular, we can identify g and g*, which we shall do whenever it is convenient.
57#
發(fā)表于 2025-3-31 11:26:28 | 只看該作者
58#
發(fā)表于 2025-3-31 13:35:41 | 只看該作者
59#
發(fā)表于 2025-3-31 18:50:48 | 只看該作者
,Some Zeta Functions Attached to ΓG/K,spectral properties of the space form Γ./. where .= SO(2). Z.(?, .), now called the ., satisfies a functional equation . → 1 → . (involving Harish-Chandra’s .-function) and, up to finite exceptions involving the possible occurrence of . representations of . in .. (Γ.), ..(?,.) satisfies a .: its “nontrivial” zeros have real part equal ?.
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