超自守形式的一个Satake型定理
A Satake type theorem for Super Automorphic forms
摘要：
本文给出了关于格的秩为1的复有界对称超区域B上的超自守形式的一个Satake型定理。这个定理--粗略地说--是说对于大权k和所有从1到无穷大的p（包括两者），B上的超自守形式是超尖点形式当且仅当它关于B的商上的某个测度的p-范数是有限的。特别地，所有这些Lp-空间都重合！我们将使用B的无界实现和通过部分凯莱变换映射到无穷大的商的尖点处的傅里叶分解来证明这个定理。
英文摘要：
Aim of this article is a Satake type theorem for super automorphic forms on a complex bounded symmetric super domain B of rank 1 with respect to a lattice. This theorem - roughly speaking - says that for large weight k and all p from 1 to infinity (both including) a super automorphic form on B is a super cusp form if and only if its p-norm with respect to a certain measure on the quotient of B is finite. And so in particular all these Lp-spaces coincide! We will give a proof of this theorem using an unbounded realization of B and Fourier decomposition at the cusps of the quotient mapped to infinity via a partial Cayley transform.
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