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Residual Spectra of Split Classical Groups and their Inner Forms

Published online by Cambridge University Press:  20 November 2018

Neven Grbac
Neven Grbac*
Affiliation:
Department of Mathematics, University of Rijeka, Omladinska 14, 51000 Rijeka, Croatia, e-mail: neven.grbac@math.uniri.hr
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Abstract

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This paper is concerned with the residual spectrum of the hermitian quaternionic classical groups $G_{n}^{\prime }$ and $H_{n}^{\prime }$ defined as algebraic groups for a quaternion algebra over an algebraic number field. Groups $G_{n}^{\prime }$ and $H_{n}^{\prime }$ are not quasi-split. They are inner forms of the split groups $\text{S}{{\text{O}}_{4n}}$ and $\text{S}{{\text{p}}_{4n}}$. Hence, the parts of the residual spectrum of $G_{n}^{\prime }$ and $H_{n}^{\prime }$ obtained in this paper are compared to the corresponding parts for the split groups $\text{S}{{\text{O}}_{4n}}$ and $\text{S}{{\text{p}}_{4n}}$.

Keywords

11F7022E55
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 61 , Issue 4 , 01 August 2009 , pp. 779 - 806
Copyright
Copyright © Canadian Mathematical Society 2012

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