Memoirs of the American Mathematical Society 2002; 63 pp; softcover Volume: 156 ISBN10: 0821827758 ISBN13: 9780821827758 List Price: US$48 Individual Members: US$28.80 Institutional Members: US$38.40 Order Code: MEMO/156/743
 Let \(F\) be a number field and \({\bf A}\) the ring of adeles over \(F\). Suppose \(\overline{G({\bf A})}\) is a metaplectic cover of \(G({\bf A})=GL(r,{\bf A})\) which is given by the \(n\)th Hilbert symbol on \({\bf A}\). According to Langlands' theory of Eisenstein series, the decomposition of the right regular representation on \(L^2\left(G(F)\backslash\overline{G({\bf A})}\right)\) can be understood in terms of the residual spectrum of Eisenstein series associated with cuspidal data on standard Levi subgroups \(\overline{M}\). Under an assumption on the base field \(F\), this paper calculates the spectrum associated with the diagonal subgroup \(\overline{T}\). Specifically, the diagonal residual spectrum is at the point \(\lambda=((r1)/2n,(r3)/2n,\cdots,(1r)/2n)\). Each irreducible summand of the corresponding representation is the Langlands quotient of the space induced from an irreducible automorphic representation of \(\overline{T}\), which is invariant under symmetric group \(\mathfrak{S}_r\), twisted by an unramified character of \(\overline{T}\) whose exponent is given by \(\lambda\). Readership Graduate students and research mathematicians interested in number theory, and the Langlands program. Table of Contents  Introduction
 Preliminaries
 Local intertwining operators
 Spectrum associated with the diagonal subgroup
 Contour integration (after MW)
 Bibliography
 Index
