2014/03/26 by Laurent Clozel, Jack A. Thorne · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Finite Group Theory Research
paper · pdf · doi:10.1112/s0010437x13007653
Abstract As the simplest case of Langlands functoriality, one expects the existence of the symmetric power Sn(π ) , where π is an automorphic representation of \rm GL(2,\mathbbA) and \mathbbA denotes the adeles of a number field F . This should be an automorphic representation of \rm GL(N,\mathbbA) ( N=n+1) . This is known for n=2,3 and 4 . In this paper we show how to deduce the general case from a recent result of J.T. on deformation theory for ‘Schur representations’, combined with expected results on level-raising, as well as another case (a particular tensor product) of Langlands functoriality. Our methods assume F totally real, and the initial representation π of classical type.