2,803 research outputs found
Quantum Reduction and Representation Theory of Superconformal Algebras
We study the structure and representations of a family of vertex algebras
obtained from affine superalgebras by quantum reduction. As an application, we
obtain in a unified way free field realizations and determinant formulas for
all superconformal algebras.Comment: 48 page
Integrable highest weight modules over affine superalgebras and Appell's function
We classify integrable irreducible highest weight representations of
non-twisted affine Lie superalgebras. We give a free field construction in the
level~1 case. The analysis of this construction shows, in particular, that in
the simplest case of the level~1 affine superalgebra the
characters are expressed in terms of the Appell elliptic function. Our results
demonstrate that the representation theory of affine Lie superalgebras is quite
different from that of affine Lie algebras.Comment: 54 page
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