Abstract
In this chapter we prove a formula for dimensions of spaces of automorphic forms which sharpens the result of Langlands and Hotta-Parthasarathy [L], [HoP2]. Let G be a connected semisimple noncompact Lie group with finite center. Let K ⊂ G be a maximal compact subgroup of G, and let Γ ⊂ G be a discrete subgroup. Assume that Γ\G is compact and that Γ acts freely on G/K. Then X = Γ\G/K is a compact smooth manifold. Furthermore, the action of G by right translation on the Hilbert space L2(Γ\G) is decomposed discretely with finite multiplicities:
Assume that rank G is equal to rank K. We calculate the multiplicity m(Γ, π) for a discrete series representation π.
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© 2006 Birkhäuser Boston
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(2006). Dimensions of Spaces of Automorphic Forms. In: Dirac Operators in Representation Theory. Mathematics: Theory & Applications. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4493-2_8
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DOI: https://doi.org/10.1007/978-0-8176-4493-2_8
Publisher Name: Birkhäuser Boston
Print ISBN: 978-0-8176-3218-2
Online ISBN: 978-0-8176-4493-2
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