Degenerate affine Hecke algebras and Yangians. (English. Russian original) Zbl 0599.20049

Drinfel’d, V. G.

Funct. Anal. Appl. 20, 58-60 (1986); translation from Funkts. Anal. Prilozh. 20, No. 1, 69-70 (1986).

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.

Reviewer: L. N. Vaserstein (University Park)

MSC:

20C08	Hecke algebras and their representations
20G05	Representation theory for linear algebraic groups
16T25	Yang-Baxter equations
17B37	Quantum groups (quantized enveloping algebras) and related deformations

Keywords:

Yangians; Hopf algebras; Yang-Baxter equation; finite-dimensional simple Lie algebra; finite-dimensional irreducible representation

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