Knapp-Stein type intertwining operators for symmetric pairs

Möllers J, Ørsted B, Oshima Y (2016)

Publication Status: Published

Publication Type: Journal article, Original article

Publication year: 2016

Journal

Advances in Mathematics Elsevier

Book Volume: 294

Pages Range: 256-306

DOI: 10.1016/j.aim.2016.02.024

Abstract

For a symmetric pair (G, H) of reductive groups we construct a family of intertwining operators between spherical principal series representations of G and H that are induced from parabolic subgroups satisfying certain compatibility conditions. The operators are given explicitly in terms of their integral kernels and we prove convergence of the integrals for an open set of parameters and meromorphic continuation. In particular, this establishes lower bounds for multiplicities of intertwining operators.We further discuss uniqueness of intertwining operators, and for the rank one cases. (G,H)=(SU(1,n;F),S(U(1,m;F)×U(n-m;F))),with F=R,C,H,O, and for the pair. (G,H)=(GL(4n,R),GL(2n,C))we show that for a certain choice of maximal parabolic subgroups our operators generically span the space of intertwiners.

Authors with CRIS profile

Jan Frahm Juniorprofessur für Mathematik (Darstellungstheorie und Operatoralgebren)

Involved external institutions

Aarhus University DK Denmark (DK) University of Tokyo JP Japan (JP)

How to cite

APA:

Möllers, J., Ørsted, B., & Oshima, Y. (2016). Knapp-Stein type intertwining operators for symmetric pairs. Advances in Mathematics, 294, 256-306. https://dx.doi.org/10.1016/j.aim.2016.02.024

MLA:

Möllers, Jan, Bent Ørsted, and Yoshiki Oshima. "Knapp-Stein type intertwining operators for symmetric pairs." Advances in Mathematics 294 (2016): 256-306.

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