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Supersymmetry in the Non-Commutative Plane
Luc Lapointe, Hideaki Ujino, Luc Vinet
The supersymmetric extension of a model introduced by Lukierski, Stichel and Zakrewski in the non-commutative plane is studied. The Noether charges associated to the symmetries are…
Free-Field Representation of Group Element for Simple Quantum Group
Alexei Morozov, Luc Vinet
A representation of the group element (also known as ``universal -matrix'') which satisfies , is given in the form $$ g = \left(\prod_{s=1}^{d_B}\phant…
On a Bosonic-Parafermionic Realization of
A. Hamid Bougourzi, Luc Vinet
We realize the current algebra at arbitrary level in terms of one deformed free bosonic field and a pair of deformed parafermionic fields. It is shown that t…
A Quantum Analogue of the Boson-Fermion Correspondence
A. Hamid Bougourzi, Luc Vinet
We review the classical boson-fermion correspondence in the context of the current algebra at level 2. This particular algebra is ideal to exhibit this correspond…
On a c-number quantum -function
A. Mironov, A. Morozov, L. Vinet
We first review the properties of the conventional -functions of the KP and Toda-lattice hierarchies. A straightforward generalization is then discussed. It corresponds to passi…
--Hypergeometric Functions in the Formalism of Free Fields
Alexei Morozov, Luc Vinet
We describe a representation of the --hypergeometric functions of one variable in terms of correlators of vertex operators made out of free scalar fields on the Riemann sphere.