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
dimagur@weizmann.ac.il
Siddhartha Sahi
Dept. of Mathematics, Rutgers University, Hill Center -- Busch Campus, 110 Frelinghuysen Road, Piscataway, NJ 08854-8019, U.S.A.
sahi@math.rugers.edu
[Abstract-pdf]
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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