Emmy-Noether-Seminar

Datum: 26-04-2019Zeit: 14:30 – 15:30Ort: Raum 04.363, Cauerstraße 11, Erlangen

Symmetry breaking for strongly spherical real reductive groups of rank one

Clemens Weiske

Abstract: A pair (G,H) of real reductive groups is called strongly spherical if H is a reductive subgroup of G and (G x H)/diag(H) is real spherical. Then considering representations pi of a real reductive algebraic group G and tau of an algebraic reductive subgroup H, the space Hom_{H}(pi|_{H},tau) of H-intertwining operators from pi to tau is finite dimensional if and only if (G,H) is strongly spherical. These operators are called symmetry breaking operators. Restricting to those pairs where G and H are of rank one and where pi and tau are spherical principal series representations, we classify all symmetry breaking operators explicitly in terms of their distribution kernels. This generalizes previous work by Kobayashi--Speh for (G,H)=(O(1,n+1),O(1,n)) to the reductive pairs (G,H) = (U(1,n+1;F),U(1,m+1;F) x F), F=CC,HH,OO and F subgroup of U(n-m;F).

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Details

Datum:
26-04-2019
Zeit:
14:30 – 15:30
Ort:

Raum 04.363, Cauerstraße 11, Erlangen

Veranstaltungskategorien:
Emmy Noether