Super boson-fermion correspondence
We establish a super boson-fermion correspondence, generalizing the classical boson-fermion correspondence in 2-dimensional quantum field theory. A new feature of the theory is the essential noncommutativity of bosonic fields. The superbosonic fields obtained by the super bosonization procedure from super fermionic fields form the affine superalgebra \~g\(\ell _{1| 1}\). The converse, super fermionization procedure, requires introduction of the super vertex operators. As applications, we give vertex operator constructions of all degenerate highest weight representations of \~g\(\ell _{1| 1}\) and of some interesting representations of \(g\ell _{\infty | \infty}({\mathbb{C}})\), and also derive some new combinatorial identities. We hope that this construction will provide a representation theoretical framework for hierarchies of super soliton equations.
scientific article; zbMATH DE number 4015778
scientific article