Repr?sentations induites d alg?bres de Hecke affines et singularit?s de R-matrices

Abstract:  We give an explicit criterion for the irreducibility of some induction products of evaluation modules of affine Hecke algebras of type A. This allows to describe the form of the zeros and poles of the trigonometric R-matrix associated to any evaluation module of U v ( b sl N ). Abridged english version --- Let b Hn (u) be the affine Hecke algebra associated to GL(n) and Hn (u) its finite-dimensional subalgebra of type An\Gamma1 . We assume that the parameter u 2 C is not a root of unity. The simple Hn (u)-modules S are parametrized by partitions of n. Let S (z) be the b Hn (u)-module obtained from S by evaluation at z 2 C . Write = ( 1 ; : : : ; r ) and 0 = (l 1 ; : : : ; l k ) (the conjugate of ). Let E = fe = i + l j \Gamma i \Gamma j + 1; 1 i r; 1 j kg denote the set of hook-lengths of and set Z = fu \Sigmae ; e 2 E g: Given finite-dimensional b Hn i (u)- modules M i ; i = 1; 2, we write M 1 fi M 2 for the induction product of M 1 and M 2 (this is then an b Hn1+...