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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Raum 04.363, Cauerstraße 11, Erlangen