Representations of Simple Lie Groups with a Free Module of Covariants.
We describe the branching rule from to , where the latter is embedded via its action on binary cubic forms. We obtain both a numerical multiplicity formula, as well as a minimal system of generators for the geometric realization of the rule.
On démontre qu’un homomorphisme d’un sous-groupe de dans ce dernier est déterminé à une conjugaison près par son caractère si satisfait à certaines conditions. C’est le cas par exemple d’un sous-groupe discret uniforme de .
Let be a local non-archimedean field. The set of all equivalence classes of irreducible spherical representations of is described in the first part of the paper. In particular, it is shown that each irreducible spherical representation is parabolically induced by an unramified character. Bernstein’s result on the irreducibility of the parabolically induced representations of by irreducible unitary ones, and Ol’shanskij’s construction of complementary series give directly a description of all...