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arXiv · 0908.4566

Super Automorphic Forms on the Super Upper Half Plane

Roland Knevel
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Abstract

The super upper half plane, this is the ordinary upper half plane with additional odd (anticommuting) directions, admits a transitive super action of a certain super Lie group G . First we define the spaces of super automorphic and cusp forms on the super upper half plane for an ordinary lattice in G and give an asymptotic formula for their dimensions for high weight. For involving also the odd directions of G we introduce local super deformation of lattices in G and show that for high weight the spaces of super automorphic and cusp forms are stable under such local super deformations.

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Roland Knevel. 2012-08-15. Super Automorphic Forms on the Super Upper Half Plane. https://arxiv.org/abs/0908.4566

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