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].
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Partially supported by NSF grant DMS-9101358
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Schwarz, G., Zhu, Cb. Invariant differential operators on symplectic grassmann manifolds. Manuscripta Math 82, 191–206 (1994). https://doi.org/10.1007/BF02567697
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DOI: https://doi.org/10.1007/BF02567697