Invariant Differential Operators on Siegel-Jacobi Space

2011/07/04 by Jae-Hyun Yang, Yang, Jae-Hyun · 2 citations
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Mathematical Analysis and Transform Methods #math.NT #msc:13A50 #msc:15A72 #msc:32Wxx

paper · pdf · doi:10.48550/arxiv.1107.0509

32 pages. arXiv admin note: substantial text overlap with arXiv:arXiv:math/0611389

arxiv created 2011/07/04 · arxiv updated 2011/12/24

Abstract

For two positive integers m and n, we let \mathbb H_n be the Siegel upper half plane of degree n and let \mathbb C^(m,n) be the set of all m× n complex matrices. In this article, we study differential operators on the Siegel-Jacobi space \mathbb H_n× \mathbb C^(m,n) that are invariant under the natural action of the Jacobi group Sp(n,\mathbb R\ltimes H_{\mathbb R}^(n,m) on \mathbb H_n× \mathbb C^(m,n), where H_{\mathbb R}^(n,m) denotes the Heisenberg group. We give some explicit invariant differential operators. We present important problems which are natural. We give some partial solutions for these natural problems.

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