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On the SL(2) period integral
DSpace at IIT Bombay
View Archive Info| Field | Value | |
| Title |
On the SL(2) period integral
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| Creator |
ANANDAVARDHANAN, UK
PRASAD, D |
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| Subject |
distinguished representations
l-indistinguishability multiplicities sl(n) |
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| Description |
Let E/F be a quadratic extension of number fields. For a cuspidal representation pi of SL2(A(E)), we study in this paper the integral of functions in pi on SL2(F)\SL2(A(F)). We characterize the nonvanishing of these integrals, called period integrals, in terms of pi having a Whittaker model with respect to characters of E\A(E) which are trivial on A(F). We show that the period integral in general is not a product of local invariant functionals, and find a necessary and sufficient condition when it is. We exhibit cuspidal representations of SL2 (AE) whose period integral vanishes identically while each local constituent admits an SL2-invariant linear functional. Finally, we construct an automorphic representation pi on SL2(A(E)) which is abstractly SL2(A(F)) distinguished but for which none of the elements in the global L-packet determined by it is distinguished by SL2(A(F)).
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| Publisher |
JOHNS HOPKINS UNIV PRESS
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| Date |
2011-08-17T02:43:07Z
2011-12-26T12:55:17Z 2011-12-27T05:44:03Z 2011-08-17T02:43:07Z 2011-12-26T12:55:17Z 2011-12-27T05:44:03Z 2006 |
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| Type |
Article
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| Identifier |
AMERICAN JOURNAL OF MATHEMATICS, 128(6), 1429-1453
0002-9327 http://dx.doi.org/10.1353/ajm.2006.0000 http://dspace.library.iitb.ac.in/xmlui/handle/10054/9712 http://hdl.handle.net/10054/9712 |
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| Language |
en
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