Multiplicity one Conjectures

Details Multiplicity one Conjectures Multiplicity one Conjectures

2007-05-15

arxiv.org/abs/0705.2168v1

Mathematics

Representation Theory

111 pages, no figures

Scientific paper

In the first part, in the local non archimedean case, we consider distributions on GL(n+1) which are invariant under the adjoint action of GL(n). We conjecture that such distributions are invariant by transposition. This would imply multiplicity at most one for restrictions from GL(n+1) to GL(n). We reduce ourselves to distributions with "singular" support and then finish the proof for n< 9. In the second part we show that similar Theorems for orthogonal or unitary groups follow from the case of GL(n)

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