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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

An analogue of Siegel's $ \phi$-operator for automorphic forms for $ {\rm GL}\sb n({\bf Z})$


Author: Douglas Grenier
Journal: Trans. Amer. Math. Soc. 333 (1992), 463-477
MSC: Primary 11F55; Secondary 11F32, 11F70
MathSciNet review: 1066443
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Abstract: If $ \mathcal{S}{P_n}$ is the symmetric space of $ n \times n$ positive matrices, $ Y \in \mathcal{S}{P_n}$ can be decomposed into

$\displaystyle Y = \left( {\begin{array}{*{20}{c}} 1 & 0 \\ x & I \\ \end{array}... ...)\left( {\begin{array}{*{20}{c}} 1 & {{T_x}} \\ 0 & I \\ \end{array} } \right),$

where $ W \in \mathcal{S}{P_{n - 1}}$ . By letting $ v \to \infty $ we obtain the $ \phi $-operator that attaches to every automorphic form for $ G{L_n}(\mathbb{Z})$, $ f(Y)$, an automorphic form for $ G{L_{n - 1}}(\mathbb{Z})$, $ f\vert\phi (W)$.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1992-1066443-0
PII: S 0002-9947(1992)1066443-0
Article copyright: © Copyright 1992 American Mathematical Society