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COMMUTATIVE SPACES WHICH ARE NOT WEAKLY SYMMETRIC

Published online by Cambridge University Press:  01 January 1998

JORGE LAURET
JORGE LAURET
Affiliation:
Facultad de Matemática, Astronomía y Física, Univ. Nac. de Córdoba, 5000 Córdoba, Argentina
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Abstract

In 1956, A. Selberg introduced weakly symmetric spaces in the framework of his development of the trace formula, and proved that in a weakly symmetric space, the algebra of all invariant (with respect to the full isometry group) differential operators is commutative [22]. In this paper, Selberg asked whether the converse holds. In the present work, we shall answer this question by presenting examples of commutative spaces which are not weakly symmetric. These examples arise in the quaternionic analogues to the Heisenberg group, endowed with certain special metrics (see Theorem 5 and the explicit realization after it).

Type
Research Article
Information
Bulletin of the London Mathematical Society , Volume 30 , Issue 1 , January 1998 , pp. 29 - 36
Copyright
© The London Mathematical Society 1998

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