Degenerate affine Hecke algebras and Yangians (Q1080521)

The Yangians is a new class of Hopf algebras introduced by the author in connection with the Yang-Baxter equation. Such an algebra \(Y({\mathfrak a})\) is defined for any finite-dimensional simple Lie algebra \(\mathfrak a\) over the complex numbers. Each finite-dimensional irreducible representation of \(Y({\mathfrak a})\) gives a quantum \(R\)-matrix, so those representations are of interest for mathematical physics. In the present paper, the case \({\mathfrak a}=\mathfrak{sl}(N)\) is studied. It is known that the representations of \({\mathfrak a}\) and the symmetric groups \(S_m\) are closely related. A similar relation between representations of \(Y({\mathfrak a})\) and certain algebras \(\Lambda_m\) is obtained.