Please use this identifier to cite or link to this item: http://scholarbank.nus.edu.sg/handle/10635/103184
Title: Eigendistributions for orthogonal groups and representations of symplectic groups
Authors: Howe, R.
Zhu, C.-B. 
Issue Date: 2002
Source: Howe, R.,Zhu, C.-B. (2002). Eigendistributions for orthogonal groups and representations of symplectic groups. Journal fur die Reine und Angewandte Mathematik (545) : 121-166. ScholarBank@NUS Repository.
Abstract: We consider the action of H = O(p, q) on the matrix space Mp+q,n(ℝ). We study a certain orbit script O sign of H in the null cone N ⊆ Mp+q,n(ℝ) which supports an eigen-distribution dvscript O sign for H. Using some identities of Capelli type developed in the Appendix, we determine the structure of G̃ = Sp(2n, ℝ)̃ -cyclic module generated by dvscript O sign under the oscillator representation of double-struck G sigñ (the metaplectic cover of double-struck G sign = Sp(2n(p + q), ℝ)). Applications to local theta correspondence and a generalized Huygens' Principle are given.
Source Title: Journal fur die Reine und Angewandte Mathematik
URI: http://scholarbank.nus.edu.sg/handle/10635/103184
ISSN: 00754102
Appears in Collections:Staff Publications

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