The aims of the project were threefold. The primary objective was to develop the representation theory of the Yangian of the general linear Lie algebra glN , and of the analogues of this Yangian for the other classical Lie algebras and superalgebras. In this direction, several important results were obtained. In particular, we classified those irreducible finite-dimensional representations of the Yangian of glN where a certain distinguished maximal commutative subalgebra acts semi-simply. The second objective was to study the theory of the affine Hecke algebras, which are dual to these Yangians in the sense of Drinfeld. Here, in particular, we developed the fusion procedure introduced earlier by Cherednik. The last objective was to apply these theories to the classical representation theory. Here we made a number of remarkable discoveries. In particular, we found the analogues of the classical Capelli identity for glN (1890) for the symplectic and orthogonal Lie algebras. Some of our printed articles are also available on the e-print archive Mathematics, see
EPSRC Grant and Duration: Advanced Research Fellowship over 60 months from 1.10.1995, reference B/95/AF/1978
For further information please contact: Professor Maxim Nazarov, Department of Mathematics, University of York, York YO10 5DD, England; maxim.nazarov@york.ac.uk