Complex structure on the smooth dual of GL(n)

Let G denote the p-adic group GL(n), let ¦(G) denote the smooth dual of G, let ¦(­) denote a Bernstein component of ¦(G) and let H(­) denote a Bernstein ideal in the Hecke algebra H(G). With the aid of Langlands parameters, we equip ¦(­) with the structure of complex algebraic variety, and prove tha...

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Bibliographic Details
Main Authors: Brodzki, Jacek (Author), Plymen, Roger (Author)
Format: Article
Language:English
Published: 2002.
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Summary:Let G denote the p-adic group GL(n), let ¦(G) denote the smooth dual of G, let ¦(­) denote a Bernstein component of ¦(G) and let H(­) denote a Bernstein ideal in the Hecke algebra H(G). With the aid of Langlands parameters, we equip ¦(­) with the structure of complex algebraic variety, and prove that the periodic cyclic homology of H(­) is isomorphic to the de Rham cohomology of ¦(­). We show how the structure of the variety ¦(­) is related to Xi's a±rmation of a conjecture of Lusztig for GL(n;C). The smooth dual ¦(G) admits a deformation retraction onto the tempered dual ¦t(G)