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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
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg – Springer Journals
Published: Apr 27, 2019
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