Details of Grant 

EPSRC Reference:	GR/K79406/02
Title:	YANGIANS AND AFFINE HECKE ALGEBRAS
Principal Investigator:	Nazarov, Professor M
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Department:	Mathematics
Organisation:	University of York
Scheme:	Standard Research (Pre-FEC)
Starts:	01 October 1996	Ends:	28 February 1998	Value (£):	54,110
EPSRC Research Topic Classifications:	Algebra & Geometry
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Summary on Grant Application Form
Yangians were introduced by V Drinfeld as quantum groups related to rational solutions of the classical Yang-Baxter equation. The Yangian Y(grN) of the Lie algebra grN admits a homomorphism onto the universal enveloping algebra U(grN). Representation theory of the Lie algebra can be regarded as a specialisation of that of Yangian. There are analogues of Yangian for the other classical Lie algebras soN and spN which admit homomorphisms onto U(soN) and U(spN) respectively. There is an analogue of the Yangian for the classical Lie superalgebra qN.A new technique was proposed by I Cherednik and E Sklyanin to study finite dimensional representations of Yangians. It employs solutions of the quantum Yang-Baxter equation and provides a new interpretation of the Schur-Weyl duality between grN and the symmetric group Sn. The aim of the project is to obtain new results on representations of the classical Lie algebras by studying Yangians. We will give new interpretation of the Littlewood-Richardson rules for decomposing the tensor products of irreducible representations of grN.We will work with objects dual to the classical Lie algebras. For the Brauer algebra dual to soN or SNP we will obtain multiplicative formulas for minimal idemmpotents. The object dual to qN is the semidirect product Sn Cn of the symmetric group by the Clifford algebra. Linear representations of this product are constructed from projective representations of Sn. By considering the Yangian of the queer Lie superalgebra we will obtain q-analogues of the Young orthogonal form and of the Young symmetrizers for the projective representations of Sn.Key Words: Combinatorics, Representation Theory, Symmetric Group, Yangians
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Organisation Website:	http://www.york.ac.uk