W-algebras in lattice vertex operator algebras

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The purpose of the project is to study the structure of the vertex operator algebras associated with positive definite even lattices. In particular, we are interested in the subalgebra consisting of the fixed points by an automorphism of finite order that is, an orbifold. More precisely, the orbifold of the vertex operator algebra associated with √<2> times an ordinary root lattice of type A_2 by an automorphism induced from the Coxeter element of the root system is studied. The orbifold contains two W_3-algebras as its subalgebras, one is of central charge 4/5 and the other is of central charge 6/5. The classification of irreducible modules for these two W_3-algebras are known. Based on the known results, we have studied the orbifold in detail and classified its irreducible modules. The results obtained in this project are published in recent papers. The results were also presented at several meetings and some international conferences. The work is concerned with the root lattice of type A_2. The case for the root lattice of type A with general rank should be an important subject