Translation principle in the category O for the Virasoro algebra
Abstract
Representations of the Virasoro algebra are the main ingredient of Conformal Field Theory. This explains a very close attention to it from physicists and mathematicians. The Virasoro algebra has many features in common with finite dimensional semi-simple Lie algebras. In particular the category O has a splitting into the direct sum of "elementary" subcategories $O\sb\theta.$ A classical result in representation theory of semi-simple Lie algebras asserts that there is a finite set of equivalence classes of subcategories $O\sb\theta.$ This is why one is led to conjecture this property for the Virasoro algebra. Very detailed knowledge of projective objects in O is the main technical moment in our approach to this problem. The main result is that this conjecture does not hold. We exhibit an invariant which distinguishes some categories which are to be equivalent due to the conjecture. We hope that our results will help to understand the real nature of the Riemann correspondence for the Virasoro algebra.
Recommended Citation
Michael V Movshev,
"Translation principle in the category O for the Virasoro algebra"
(January 1, 1997).
Dissertations available from ProQuest.
Paper AAI9727264.
http://repository.upenn.edu/dissertations/AAI9727264
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