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Journal of Lie Theory 23 (2013), No. 4, 1191--1200
Copyright Heldermann Verlag 2013

Intertwining Operators Between Line Bundles on Grassmannians

Dmitry Gourevitch
Faculty of Mathematics and Computer Science, Weizmann Institute of Science, POB 26, Rehovot 76100, Israel

Siddhartha Sahi
Dept. of Mathematics, Rutgers University, Hill Center -- Busch Campus, 110 Frelinghuysen Road, Piscataway, NJ 08854-8019, U.S.A.


Let $G={\rm GL}(n,F)$ where $F$ is a local field of arbitrary characteristic, and let $\pi_{1},\pi_{2}$ be representations induced from characters of two maximal parabolic subgroups $P_{1},P_{2}$. We explicitly determine the space ${\rm Hom}_{G}\left(\pi_{1},\pi_{2}\right)$ of intertwining operators and prove that it has dimension $\leq1$ in all cases.

Keywords: Reductive group, maximal parabolic, degenerate principal series, derivatives of representations, Radon transform, cosine transform.

MSC: 22E50, 44A05, 44A12

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