Mautner's lemma

In mathematics, Mautner's lemma in representation theory states that if G is a topological group and π a unitary representation of G on a Hilbert space H, then for any x in G, which has conjugates

yxy−1

converging to the identity element e, for a net of elements y, then any vector v of H invariant under all the π(y) is also invariant under π(x).

References
  • F. Mautner, Geodesic flows on symmetric Riemannian spaces (1957), Ann. Math. 65, 416-430
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