Vol. 86, No. 1, 1980

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The Mautner phenomenon for general unitary representations

Calvin Cooper Moore

Vol. 86 (1980), No. 1, 155–169

The ‘Mautner phenomenon’ for unitary representations is a general assertion of the form that if x(t) is a one parameter subgroup of a Lie group G, π a unitary representation of G on a Hilbert space = (π) and v a vector in which is fixed by x(t); i.e., π(x(t))v = v, then v must also be fixed by a generally much larger subgroup H of G. How much larger H is than the original one parameter group depends in a general way on how noncommutative the group G is. Our purpose here is to establish a very general result of this nature which we believe to be the best possible result of this kind.

Mathematical Subject Classification 2000
Primary: 22E45
Received: 15 March 1979
Published: 1 January 1980
Calvin Cooper Moore