publication . Preprint . 2005

Division Algebras and Non-Commensurable Isospectral Manifolds

Lubotzky, Alexander; Samuels, Beth; Vishne, Uzi;
Open Access English
  • Published: 05 Jan 2005
Abstract
Comment: 22 pages
Subjects
arXiv: Mathematics::Representation TheoryMathematics::Group TheoryMathematics::Algebraic GeometryMathematics::ProbabilityMathematics::Geometric Topology
free text keywords: Mathematics - Spectral Theory, Mathematics - Representation Theory, 58J53, 11F72
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25 references, page 1 of 2

By Theorem 3, L2(G′1(k)\G0) ∼= L2(G′2(k)\G0) as representation spaces, so the result follows.

Let us now define a map JL0, which takes an irreducible infinitedimensional sub-representation π′′ of L2(Δ\G0) to an irreducible infinitedimensional sub-representation π of L2(G(k)\G(A)), which occurs in [AT] E. Artin and J. Tate, Class Field Theory, W.A. Benjamin, 1967.

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[Br2] R. Brooks, The Sunada method, Tel Aviv Topology Conference: Rothenberg Festschrift (1998), 25-35, Contemp. Math., 231, Amer. Math. Soc., Providence, RI, 1999.

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[H] S. Helgason, Differential Geometry and Symmetric Spaces, Academic Press, 1962.

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[LSV1] A. Lubotzky, B. Samuels and U. Vishne, Ramanujan complexes of type A˜d, Israel J. of Math., to appear.

[LSV2] A. Lubotzky, B. Samuels and U. Vishne, Isospectral Cayley graphs of some simple groups, preprint.

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