K-theory for Sp(n, 1)

The classification of unitary irreducible representations of G = Sp(n, 1), (n 2), is done by Baldoni-Silva [Duke Math. J. 48 (3) (1981) 549–583]. In particular, there are Langlands quotients that do not appear in the continuous complementary series. They are called isolated series. Let :C∗max(G) → C∗red(G) be the regular representation. In this article we show that the representation ⊕ (⊕ ), where runs over the set of isolated series, induces an isomorphism in K-theory. In particular, the kernel of the map induced by in K-theory, is a free Zmodule with a set of generators in bijective correspondence with the set of isolated series. Let K be a maximal compact subgroup of G, and let R(K) be its representation ring. We then compute the range of the full Baum–Connes map R(K) → K0(C∗max(G)) in terms of these generators. © 2004 Elsevier Inc. All rights reserved.