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A central extension of \(DY_{\hbar}(\mathfrak{gl}_ 2)\). (English) Zbl 0867.17013

The authors define a central extension \(DY_\hbar ({\mathfrak {gl}}_2)\) of the quantum double of the Yangian of \({\mathfrak {gl}}_2\), using the ‘RTT formalism’. Drinfeld generators for \(DY_\hbar ({\mathfrak {gl}}_2)\) are also given. An analogue for \(DY_\hbar ({\mathfrak {gl}}_2)\) of the bosonic construction of the level 1 highest weight modules for (quantum) affine \({\mathfrak {gl}}_2\) is then given. This is used to define vertex operators and compute their commutation relations.

MSC:

17B37 Quantum groups (quantized enveloping algebras) and related deformations
81R50 Quantum groups and related algebraic methods applied to problems in quantum theory
17B67 Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras
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