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# Residual Spectra of Split Classical Groups and their Inner Forms

Published:2009-08-01
Printed: Aug 2009
• Neven Grbac
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## Abstract

This paper is concerned with the residual spectrum of the hermitian quaternionic classical groups $G_n'$ and $H_n'$ defined as algebraic groups for a quaternion algebra over an algebraic number field. Groups $G_n'$ and $H_n'$ are not quasi-split. They are inner forms of the split groups $\SO_{4n}$ and $\Sp_{4n}$. Hence, the parts of the residual spectrum of $G_n'$ and $H_n'$ obtained in this paper are compared to the corresponding parts for the split groups $\SO_{4n}$ and $\Sp_{4n}$.
 MSC Classifications: 11F70 - Representation-theoretic methods; automorphic representations over local and global fields 22E55 - Representations of Lie and linear algebraic groups over global fields and adele rings [See also 20G05]