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International Journal of Functional Analysis, Operator Theory and Applications

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 that of

Here the disintegration map of the covariant 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

International Journal of Functional Analysis, Operator Theory and Applications
Volume 3, Issue 1, Pages 53 - 69 (June 2011)

INVARIANT DIFFERENTIAL OPERATORS AND ANNIHILATORS OF COVARIANT DISTRIBUTION VECTORS
Mamour Sankhe

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 that of

Here the disintegration map of the covariant 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.

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