Application of Vertex Algebras to the Structure Theory of Certain Representations Over the Virasoro Algebra

作者：Radobolja Gordan^*

来源：Algebras and Representation Theory, 2014, 17(4): 1013-1034.

DOI：10.1007/s10468-013-9428-9

• Virasoro algebra
• Highest weight module
• Intermediate series
• Minimal model
• Vertex operator algebra
• Intertwining operator

In this paper, we discuss the structure of the tensor product of an irreducible module from an intermediate series and irreducible highest-weight module over the Virasoro algebra. We generalize Zhang's irreducibility criterion from Zhang (J Algebra 190:1-10, 1997), and show that irreducibility depends on the existence of integral roots of a certain polynomial, induced by a singular vector in the Verma module V(c,h). A new type of irreducible Vir-module with infinite-dimensional weight subspaces is found. We show how the existence of intertwining operators for modules over vertex operator algebra yields reducibility of , which is a completely new point of view to this problem. As an example, the complete structure of the tensor product with minimal models c = -aEuro parts per thousand 22/5 and c = 1/2 is presented.

• 出版日期2014-8