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Analytic vectors and irreducible representations of nilpotent Lie groups and algebras

โœ Scribed by D. Arnal

Publisher
Springer
Year
1978
Tongue
English
Weight
240 KB
Volume
2
Category
Article
ISSN
0377-9017

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โœฆ Synopsis

Let U be a unitary irreducible locally faithful representation of a nilpotent Lie group G, ~ the universal enveloping algebra of G, M a simple module on o//with kernel Ker dU, then there exists an automorphism of q/keeping ker dU invariant such that, after transport of structure, M is isomorphic to a submodule of the space of analytic vectors for U.

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## RESTRICTION OF REPRESENTATIONS with Q-linearly independent real numbers : 1 , : 2 . Then By Proposition 1.1, r l is not contained in a proper rational ideal of g. So, ? l | 1 is irreducible, by Theorem 1.1. Now, if f =n 4 X 4 \*+n 5 X 5 \* # g\* with n 4 , n 5 # Z&[0] then it is easy to see th