Rational differential forms on line and singular vectors in Verma modules over \widehat sl₂

2015/11/29 by Schechtman, Vadim, Varchenko, Alexander
#Algebraic Geometry (math.AG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.1511.09014

Abstract

We construct a monomorphism of the De Rham complex of scalar multivalued meromorphic forms on the projective line, holomorphic on the complement to a finite set of points, to the chain complex of the Lie algebra of sl₂-valued algebraic functions on the same complement with coefficients in a tensor product of contragradient Verma modules over the affine Lie algebra sl₂. We show that the existence of singular vectors in the Verma modules (the Malikov-Feigin-Fuchs singular vectors) is reflected in the new relations between the cohomology classes of logarithmic differential forms.

Related

• Differential Equations for Singular Vectors of sl(n)
• Differential-Operator Representations of S_n and Singular Vectors in Verma Modules
• The product on \W-spaces of rational forms
• Logarithmic forms with twisted coefficients
• Space of second order linear differential operators as a module over the Lie algebra of vector fields