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Topologically irreducible representations of the Schwartz-algebra of a nilpotent Lie group

✍ Scribed by Jean Ludwig


Book ID
112494876
Publisher
Springer
Year
1990
Tongue
English
Weight
415 KB
Volume
54
Category
Article
ISSN
0003-889X

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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

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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