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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
2002.
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| Subjects: | |
| Online Access: | Get fulltext |
| 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) |
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