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B L Feigin

Publications and source records attributed to B L Feigin.

3 recordsLinked to original sources
arXiv1998

Free-Field Resolutions of the Unitary N=2 Super-Virasoro Representations

We construct free-field resolutions of unitary representations of the N=2 superconformal algebra. The irreducible representations are singled out from free-field spaces as the cohomology of fermionic screening operators. We construct and evaluate the cohomology of the resolution associated with one fermionic screening (which is related to the representation theory picture of ``gravitational descendants''), and a {\it butterfly} resolution associated with two fermionic screenings.

hep-th↗
arXiv1998

Resolutions and Characters of Irreducible Representations of the N=2 Superconformal Algebra

We evaluate characters of irreducible representations of the N=2 supersymmetric extension of the Virasoro algebra. We do so by deriving the BGG-resolution of the admissible N=2 representations and also a new 3,5,7...-resolution in terms of twisted massive Verma modules. We analyse how the characters behave under the automorphisms of the algebra, whose most significant part is the spectral flow transformations. The possibility to express the characters in terms of theta functions is determined by their behaviour under the spectral flow. We also derive the identity expressing every $\hat{sl}(2)$ character as a linear combination of spectral-flow transformed N=2 characters; this identity involves a finite number of N=2 characters in the case of unitary representations. Conversely, we find an integral representation for the admissible N=2 characters as contour integrals of admissible $\hat{sl}(2)$ characters.

hep-th↗