Orthogonal polynomial bases for holomorphically induced representations of the general linear groups

Key-words : Free group - Uniformly bounded representations... parametrized by spherical functions was given. There arises a prob- lem of finding the theorem for a free group related

Holomorphic induction and the tensor product decomposition of irreducible representations of compact groups..

possible extensions to the group IO(n) are different for integer or half- integer values of the discrete labels which specify an IR of the identity component

From the knowledge of the representation theory of G 4 , it is easy to determine from the infinites- imal data whether the corresponding monodromy representation factorize through

In Section 6, we prove that any analytic representation of a semi-simple Lie group in a finite-dimensional space is banal, and that any analytic representation of a nilpotent Lie

For instance, by what we saw above, the left (or right) regular representation of a connected solvable Lie group always has this property. Our results imply, that an « overwhelming

have verified that the spectrum and multiplicity portions of the orbital spectrum formula are valid. Therefore 7r is not induced from Go. Hence 7r itself must

for compact semisimple Lie groups an irreducible representation is completely determined by its infinitesimal character, but that this is far from true for nilpotent Lie