Holomorphic induction and the tensor product decomposition of irreducible representations of compact groups. I. <span class="mathjax-formula">$SU(n)$</span> groups

In order to obtain the representation \, r&gt;0, referred to just prior to Lemma 5.6, one must imitate Waldspurger's construction of © and K alluded to above.

subgroup U^ c G^ ofunipotent upper triangular matrices such that co may in a unique way be embedded into the representation of G^, induced by 6 (for non-degenerate (D this was done

ANNALES SCIENTIFIQUES DE L'ECOLE NORMALE SUPERIEURE 61.. We begin to prove our Lemmas. — Use the Bruhat decomposition.. For the computation of the functor F from 2.12 use the

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

Regular characters of a maximal split torus in a split reductive group, for which corresponding non-unitary principal series representations have square.. integrable

Keywords: nilpotent p-adic Lie group, square integrable irreducible representation, supercuspidal representation, induced representation, compact open

that the restriction of an irreducible unitary representation of G to its subspace of smooth vectors is an admissible representation of

We recall here the definition of induced (unitary) representations, some analysis on locally compact fields k and the definition and some properties.. of locally