Singular vectors and their connection to symmetric polynomials
Singular vectors in Verma modules over algebras such as the Virasoro algebra or affine Lie algebras are of vital importance to conformal field theory as they are important tools for understanding the representation theory of chiral algebras and computing correlation functions. Unfortunately explicit formulae for singular vectors are notoriously hard to come by. In this talk I will explain how such formulae can be obtained using free field theories, so called screening operators and their connection to the very rich field of symmetric polynomials.
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