# On a symmetry of the category of integrable modules - Mathematics > Quantum Algebra

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Abstract: Haisheng Li showed that given a module W,Y W\cdot,x for a vertex algebraV,Y\cdot,x, one can obtain a new V-module W^{\Delta} =W,Y W\Deltax\cdot,x if \Deltax satisfies certain natural conditions. Lipresented a collection of such \Delta-operators for V=Lk,0 a vertex operatoralgebra associated with an affine Lie algebras, k a positive integer. In thispaper, for each irreducible Lk,0-module W, we find a highest weight vector ofW^{\Delta} when \Delta is associated with a miniscule coweight. From this wecompletely determine the action of these \Delta-operators on the set ofisomorphism equivalence classes of Lk,0-modules.

Author: ** William J. Cook, Christopher Sadowski**

Source: https://arxiv.org/