International Congress of Mathematicians

Representations of Yangians 6532.4. Let us extend a to an automorphism of the associative algebra \J(gt N ). Forany z £ C, define the twisted evaluation module V(z) over the algebra Y(gl JV ) bypullingthe standard action of the algebra \J(gt N ) in the vector space C^ backthrough the composition of homomorphismsa o a N ° T- z : Y(gl N ) -+ Y(gl N ).The evaluation module V(z) and the twisted evaluation module V(z) over Y(gl N ),have the same restriction to the subalgebra Y(gl N ,a) C Y(gl N ); see (2.1).For any A and p, the operator FQ(M) has the following interpretation in termsof the restrictions to Y(gl N ,a) of tensor products of evaluation modules over theHopf algebra Y(gl N ); cf. Proposition 2. For each k = 1, ..., n put dk = Ck + ^ -\-We assume that A{ + X' 2 ^ N + M and p[ + p' 2 ^ M.Proposition 4. The operator FQ(M) is an intertwiner ofY(gl N ,a)-modulesV(di) ®...® V(d n ) —y V(di) ®...® V(d n ).By Proposition 4, the image of FQ(M) is a submodule in the restriction of thetensor product of evaluation Y(gl JV )-modules V(di)®... ® V(d n ) to the subalgebraY(gljvj