Residual Spectra of Split Classical Groups and their Inner Forms

Grbac, Neven

Canadian journal of mathematics, Tome 61 (2009) no. 4, pp. 779-806

Résumé

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 $\text{S}{{\text{p}}_{4n}}$ .

Détail

DOI : 10.4153/CJM-2009-042-3

Mots-clés : 11F70, 22E55

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