## 2006.105: Complex structure on the smooth dual of GL(n)

2006.105:
Jacek Brodzki and Roger Plymen
(2002)
*Complex structure on the smooth dual of GL(n).*
Documenta Mathematica, 7.
pp. 91-112.
ISSN 1431-0643

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Official URL: http://www.math.uiuc.edu/documenta/vol-07/04.html

## Abstract

Let G denote the p-adic group GL(n). With the aid of Langlands parameters, we equip each Bernstein component Z in the smooth dual of G with the structure of complex algebraic variety. We prove that the periodic cyclic homology of the corresponding ideal in the Hecke algebra H(G) is isomorphic to the de Rham cohomology of Z. We show how the structure of the variety Z is related to Xi's affirmation of a conjecture of Lusztig for GL(n,C). The smooth dual of G admits a deformation retraction onto the tempered dual of G.

Item Type: | Article |
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Uncontrolled Keywords: | General linear group. Langlands parameters. Hecke algebra. Smooth dual. Tempered dual. |

Subjects: | MSC 2000 > 18 Category theory; homological algebra MSC 2000 > 22 Topological groups, Lie groups MSC 2000 > 43 Abstract harmonic analysis |

MIMS number: | 2006.105 |

Deposited By: | Professor Roger Plymen |

Deposited On: | 19 May 2006 |

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