Coma704
发表于 2025-3-28 16:49:15
Finite-Dimensional Representation Theoryl Theorem for compact semisimple groups in Section 15. Finally, in Section 16, we specialize to the decomposition of the . space of a compact symmetric space and give Cartan’s highest weight theory for class one representations.
Commission
发表于 2025-3-28 22:39:43
http://reply.papertrans.cn/43/4243/424271/424271_42.png
Adrenal-Glands
发表于 2025-3-29 02:26:25
General Backgroundions: (1) What sort of regularity properties should . possess for the decomposition to make any sense at all?; (2) In what sense does the series converge? These questions (or their analogues) will persist throughout our investigations.
连系
发表于 2025-3-29 04:56:00
Infinite-Dimensional Representationsct subgroup . ⊂ G has multiplicity .(к, π|.) ≤ dim к. This yields up the infinitesimal character χ.: .(g)→ ℂ and the distribution character .: C.(G) → ℂ, and consequently the differential equations. for .which are the starting point for serious harmonic analysis on ..
弯曲的人
发表于 2025-3-29 10:32:57
Nonlinear Representations of Lie Groups and ApplicationsStill, what more specific motivations do we have to study nonlinear representations of Lie groups in linear spaces? We may of course reverse the argument and ask why in the past did we study mainly linear representations of a nonlinear object?!
Ethics
发表于 2025-3-29 14:01:29
http://reply.papertrans.cn/43/4243/424271/424271_46.png
Meditate
发表于 2025-3-29 18:41:56
http://reply.papertrans.cn/43/4243/424271/424271_47.png
刀锋
发表于 2025-3-29 19:56:43
http://reply.papertrans.cn/43/4243/424271/424271_48.png
BRAWL
发表于 2025-3-30 00:47:36
Infinite-Dimensional Representations.. The basic fact for an irreducible unitary representation . of . on a Hilbert space ℋ, is that every irreducible representation к of a maximal compact subgroup . ⊂ G has multiplicity .(к, π|.) ≤ dim к. This yields up the infinitesimal character χ.: .(g)→ ℂ and the distribution character .: C.(G) →
breadth
发表于 2025-3-30 05:56:46
http://reply.papertrans.cn/43/4243/424271/424271_50.png