Let T be a homogeneous tree of degree 3, let G be the automorphism group of T, and let π+ and π- be the special representations of G. We consider two discrete subgroups of G isomorphic to Z3 * Z3 and Z2 * Z2 * Z2 and show how to decompose into irreducibles the restrictions of π+ and π- to these subgroups. We also present a general formula relating continuous dimension for representations of discrete groups and formal dimension for representations of continuous groups
Kuhn, M., Steger, T. (1992). Restrictions of the special representation of ${\rm Aut}({\rm tree}\sb 3)$ to two cocompact subgroups. ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 22(4), 1349-1363 [10.1216/rmjm/1181072661].
Restrictions of the special representation of ${\rm Aut}({\rm tree}\sb 3)$ to two cocompact subgroups
KUHN, MARIA GABRIELLA;
1992
Abstract
Let T be a homogeneous tree of degree 3, let G be the automorphism group of T, and let π+ and π- be the special representations of G. We consider two discrete subgroups of G isomorphic to Z3 * Z3 and Z2 * Z2 * Z2 and show how to decompose into irreducibles the restrictions of π+ and π- to these subgroups. We also present a general formula relating continuous dimension for representations of discrete groups and formal dimension for representations of continuous groupsI documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.