Residual Spectra of Split Classical Groups and their Inner Forms

http://dx.doi.org/10.4153/CJM-2009-042-3
Canad. J. Math. 61(2009), 779-806

  Published:2009-08-01
 Printed: Aug 2009

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 $\Sp_{4n}$.