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

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.

### 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
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### References:

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