International Journal of Functional Analysis, Operator Theory and Applications
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Abstract: Let be the Hilbert space of an induced
unitary representation t by a character c of a connected and simply connected subgroup H
of a nilpotent Lie group G. If and h
are the respective Lie algebras of G
and H, then for some the dual of There exists an orbital description
of the irreducible representations (the dual group of G)
appearing in within this case the multiplicities finitely bounded. On the vectors space, is defined a covariant distribution
vector whose direct integral decomposition
is induced by thatof Here the disintegration map of thecovariant distribution vectors space is studied where is a covariant subspace of the antidual of and the affine variety of is the orthogonal of h.
The linear map W allows to exhibit annihilators of the so-called Frobenius vectors
Keywords and phrases: nilpotent Lie group, direct integral decomposition, unitary representation, induced representation, invariant differential operators.
