Multiplicity formulas for discrete series of Spin(1,2m) and SU(1,n)

Yasuko Konno
Introduction. Let G be a connected semisimple Lie group with finite center. Let Γ be a discrete subgroup of G such that Γ\G is compact. Assume that Γ has no elements with finite order other than the identity. Fix a Haar measure dg on G. Then dg induces the G-invariant measure on T\G and we can construct the right regular representation zr Γ of G on L 2 (Γ\G). If is wellknown that π Γ decomposes into the direct sum of irreducible unitary representations with finite multiplicity, up to unitarily
more » ... y, up to unitarily equivalence. Let G be the set of all equivalence classes of irreducible unitary representations of G. For U^:O y denote by N r (U) the multiplicity of U in π Γ .
doi:10.18910/10902 fatcat:fdab4s57yravnlj4bgapnrpemm