Abstract.
Let K be an algebraic number field, and let GK be the group of K-rational points of a simply connected simple linear algebraic group G defined over K. We construct a new family of irreducible unitary representations of GK as follows. It is well known that GK embeds diagonally as a lattice in GA, where A is the ring of adèles of K. Let be an irreducible unitary representation of GA. We show that , the restriction of to GK, is irreducible and that is determined by up to unitary equivalence. Many of these restrictions are not in the support of the regular representation of GK.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received: 17 October 2001; in final form: 8 January 2002 / Published online: 6 August 2002
Rights and permissions
About this article
Cite this article
Bekka, M., Cowling, M. Some irreducible unitary representations of G(K) for a simple algebraic group G over an algebraic number field K . Math. Z. 241, 731–741 (2002). https://doi.org/10.1007/s00209-002-0442-6
Issue Date:
DOI: https://doi.org/10.1007/s00209-002-0442-6