New York Journal of Mathematics
Volume 15 (2009) 133-160


William J. Cook and Christopher M. Sadowski

On a symmetry of the category of integrable modules

Published: April 26, 2009
Keywords: affine Lie algebras; vertex operator algebras
Subject: 17B10, 17B67, 17B69

Haisheng Li showed that given a module (W,YW(⋅,x)) for a vertex algebra (V,Y(⋅,x)), one can obtain a new V-module
WΔ = (W,YW(Δ(x)⋅,x))
if Δ(x) satisfies certain natural conditions. Li presented a collection of such Δ-operators for V=L(k,0) (a vertex operator algebra associated with an affine Lie algebra, k a positive integer). In this paper, for each irreducible L(k,0)-module W, we find a highest weight vector of WΔ when Δ is associated with a minuscule coweight. From this we completely determine the action of these Δ-operators on the set of isomorphism equivalence classes of L(k,0)-modules.


C. Sadowski acknowledges support from the the Rutgers Mathematics/DIMACS REU Program during the summers of 2007 and 2008, and NSF grant DMS-0603745.

Author information

William J. Cook:
Department of Mathematical Sciences, Appalachian State University, Boone, NC 28608

Christopher M. Sadowski:
Department of Mathematics, Rutgers University, Piscataway, NJ 08854