Vertex representations of quantum affine algebras. (English) Zbl 0662.17006

Vertex representations of quantum affine algebras of ADE type are constructed in this paper. These algebras were first introduced in greater generality by Drinfeld and Jimbo. The limiting special case of this construction is the untwisted vertex representation of affine Lie algebras of Frenkel-Kac and Segal. The representation in this paper is given by means of a new type of vertex operator corresponding to the simple roots and satisfying the defining relations. The quantum affine algebras of type A are dealt with in more detail.


17B37 Quantum groups (quantized enveloping algebras) and related deformations
17B67 Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras
17B69 Vertex operators; vertex operator algebras and related structures
16T20 Ring-theoretic aspects of quantum groups
16T25 Yang-Baxter equations
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