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.


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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