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On representations of GL(n) distinguished by GL(n-1) over a p-adic field

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Title On representations of GL(n) distinguished by GL(n-1) over a p-adic field
 
Creator VENKETASUBRAMANIAN, CG
 
Subject IRREDUCIBLE REPRESENTATIONS
GL(2)
 
Description For a nonarchimedean local field F, let GL(n):= GL(n, F) and GL(n-1) be embedded in GL(n) via g a dagger broken vertical bar ( (0 1) (g 0) ). Let pi be an irreducible admissible representation of GL(n) for n a parts per thousand yen 3. We prove that pi is GL(n - 1)-distinguished if and only if the Langlands parameter L(pi) associated to pi by the Local Langlands Correspondence has a subrepresentation L(11 (n-2)) of dimension n-2 corresponding to the trivial representation of GL(n-2) such that the two-dimensional quotient L(pi)/L(11 (n-2)) corresponds either to an infinite-dimensional representation or the one-dimensional representations of GL(2). We also prove that, for a parabolic subgroup P of GL(n) and an irreducible admissible representation rho of the Levi subgroup of P, . For the standard Borel subgroup B (n) of GL(n) and characters x (i) of GL(1), we classify all representations xi of the form for which dim(C)(Hom(GL(n-1))[xi, ll(n-1)]) = 2.
 
Publisher HEBREW UNIV MAGNES PRESS
 
Date 2014-10-14T13:05:54Z
2014-10-14T13:05:54Z
2013
 
Type Article
 
Identifier ISRAEL JOURNAL OF MATHEMATICS, 194(1)1-44
http://dx.doi.org/10.1007/s11856-012-0152-7
http://dspace.library.iitb.ac.in/jspui/handle/100/14477
 
Language en