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One-line formula for automorphic differential operators on Siegel modular forms

One-line formula for automorphic differential operators on Siegel modular forms We consider the Siegel upper half space H of degree 2m and a subset H × H of H 2m m m 2m consisting of two m × m diagonal block matrices. We consider two actions of Sp(m, R) × Sp(m, R) ⊂ Sp(2m, R), one is the action on holomorphic functions on H defined by 2m the automorphy factor of weight k on H and the other is the action on vector valued 2m holomorphic functions on H × H defined on each component by automorphy factors m m obtained by det ⊗ρ,where ρ is a polynomial representation of GL(n, C). We consider vector valued linear holomorphic differential operators with constant coefficients on holomorphic functions on H which give an equivariant map with respect to the above two actions under 2m the restriction to H × H . In a previous paper, we have already shown that all such operators m m can be obtained either by a projection of the universal automorphic differential operator or alternatively by a vector of monomial basis corresponding to the partition 2m = m +m.Here in this paper, based on a completely different idea, we give much simpler looking one-line formula for http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Springer Journals

One-line formula for automorphic differential operators on Siegel modular forms

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References (24)

Publisher
Springer Journals
Copyright
Copyright © 2019 by The Author(s), under exclusive licence to Mathematisches Seminar der Universität Hamburg
Subject
Mathematics; Mathematics, general; Algebra; Differential Geometry; Number Theory; Topology; Geometry
ISSN
0025-5858
eISSN
1865-8784
DOI
10.1007/s12188-019-00202-x
Publisher site
See Article on Publisher Site

Abstract

We consider the Siegel upper half space H of degree 2m and a subset H × H of H 2m m m 2m consisting of two m × m diagonal block matrices. We consider two actions of Sp(m, R) × Sp(m, R) ⊂ Sp(2m, R), one is the action on holomorphic functions on H defined by 2m the automorphy factor of weight k on H and the other is the action on vector valued 2m holomorphic functions on H × H defined on each component by automorphy factors m m obtained by det ⊗ρ,where ρ is a polynomial representation of GL(n, C). We consider vector valued linear holomorphic differential operators with constant coefficients on holomorphic functions on H which give an equivariant map with respect to the above two actions under 2m the restriction to H × H . In a previous paper, we have already shown that all such operators m m can be obtained either by a projection of the universal automorphic differential operator or alternatively by a vector of monomial basis corresponding to the partition 2m = m +m.Here in this paper, based on a completely different idea, we give much simpler looking one-line formula for

Journal

Abhandlungen aus dem Mathematischen Seminar der Universität HamburgSpringer Journals

Published: Apr 27, 2019

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