Invariant differential operators on symplectic grassmann manifolds |
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Authors: | Gerald Schwarz Chen-bo Zhu |
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Institution: | (1) Department of Mathematics, Brandeis University, PO Box 9110, 02254-9110 Waltham, MA;(2) Department of Mathematics, National University of Singapore, Kent Ridge, 0511 Singapore |
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Abstract: | LetM
2n,r
denote the vector space of real or complex2n×r matrices with the natural action of the symplectic group Sp
2n
, and letG=G
n,r
=Sp
2n
×M
2n,r
denote the corresponding semi-direct product. For any integerp with 0≤p≤n−1, letH denote the subgroupG
p,r
×Sp
2n−2p
ofG. We explicitly compute the algebra of left invariant differential operators onG/H, and we show that it is a free algebra if and only ifr≤2n−2p+1. We also give orthogonal analogues of these results, generalizing those of Gonzalez and Helgason 3].
Partially supported by NSF grant DMS-9101358
This article was processed by the author using the Springer-Verlag TEX mamath macro package 1990. |
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Keywords: | |
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