naa a22 4500 510783325 CHVBK 20180411083254.0 cr unu---uuuuu 180411e20130301xx s 000 0 eng 10.1007/s11856-012-0152-7 doi (NATIONALLICENCE)springer-10.1007/s11856-012-0152-7 Venketasubramanian C. Department of Mathematics, Indian Institute of Technology Bombay, 400076, Mumbai, India aut On representations of GL( n ) distinguished by GL( n − 1) over a p -adic field [Elektronische Daten] [C. Venketasubramanian] For a nonarchimedean local field F, let GL(n):= GL(n, F) and GL(n−1) be embedded in GL(n) via g ↦ ( 0 1 g 0 ). Let π be an irreducible admissible representation of GL(n) for n ≥ 3. We prove that π is GL(n − 1)-distinguished if and only if the Langlands parameter L(π) associated to π 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(π)/L(11 n−2) corresponds either to an infinite-dimensional representation or the one-dimensional representations $\nu ^{ \pm (\tfrac{{n - 2}}{2})} $ of GL(2). We also prove that, for a parabolic subgroup P of GL(n) and an irreducible admissible representation ρ of the Levi subgroup of P, $\dim _\mathbb{C} (Hom_{GL(n - 1)} [ind_P^{GL(n)} (\rho ),\mathbb{I}_{n - 1} ]) \leqslant 2$ . For the standard Borel subgroup B n of GL(n) and characters x i of GL(1), we classify all representations ξ of the form $ind_{B_n }^{GL(n)} (\chi _1 \otimes \cdots \otimes \chi _n )$ for which $\dim _\mathbb{C} (Hom_{GL(n - 1)} [\xi ,\mathbb{I}_{n - 1} ]) = 2$ . Hebrew University Magnes Press, 2012 Israel Journal of Mathematics The Hebrew University Magnes Press 194/1(2013-03-01), 1-44 0021-2172 194:1<1 2013 194 11856 https://doi.org/10.1007/s11856-012-0152-7 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11856-012-0152-7 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Venketasubramanian C. Department of Mathematics, Indian Institute of Technology Bombay, 400076, Mumbai, India aut NATIONALLICENCE 773 0- Israel Journal of Mathematics The Hebrew University Magnes Press 194/1(2013-03-01), 1-44 0021-2172 194:1<1 2013 194 11856 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer