 

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 


Abstract
Haisheng Li showed that given a module (W,Y_{W}(⋅,x)) for a vertex algebra
(V,Y(⋅,x)), one can obtain a new Vmodule
W^{Δ} = (W,Y_{W}(Δ(x)⋅,x))
if Δ(x) satisfies certain natural conditions. Li presented a collection of
such Δoperators 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 W^{Δ} when Δ is
associated with a minuscule coweight. From this we completely determine the
action of these Δoperators on the set of isomorphism equivalence classes of
L(k,0)modules.


Acknowledgements
C. Sadowski acknowledges support from the the Rutgers Mathematics/DIMACS REU Program during the summers of 2007 and 2008, and NSF grant DMS0603745.


Author information
William J. Cook:
Department of Mathematical Sciences, Appalachian State University, Boone, NC 28608
cookwj@appstate.edu
Christopher M. Sadowski:
Department of Mathematics, Rutgers University, Piscataway, NJ 08854
sadowski@math.rutgers.edu

