Möllers J, Ørsted B, Oshima Y (2016)
Publication Status: Published
Publication Type: Journal article, Original article
Publication year: 2016
Book Volume: 294
Pages Range: 256-306
DOI: 10.1016/j.aim.2016.02.024
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.
APA:
Möllers, J., Ørsted, B., & Oshima, Y. (2016). Knapp-Stein type intertwining operators for symmetric pairs. Advances in Mathematics, 294, 256-306. https://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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