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William J. Cook and Christopher M. Sadowski
On a symmetry of the category of integrable modules
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| Published: |
April 26, 2009
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| Keywords: |
affine Lie algebras; vertex operator algebras |
| Subject: |
17B10, 17B67, 17B69 |
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Abstract
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.
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| Acknowledgements
C. Sadowski acknowledges support from the the Rutgers Mathematics/DIMACS REU Program during the summers of 2007 and 2008, and NSF grant DMS-0603745.
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| 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
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