Fock space representations of Virasoro algebra and intertwining operators
The Virasoro algebra \(L\) is the Lie algebra over the complex numbers with generators \(e_ 0'\), \(e_ n\) (where \(n\) ranges over the integers) and the relations: \(e_ 0'\) commutes with everything, \[ [e_ n, e_ m]=(m- n)e_{n+m}+\delta_{n+m}((m^ 3-m)/12)e_ 0'. \] It is a central extension of the Lie algebra of polynomial vector fields on the circle. It appears in string models of elementary particle physics. Quite recently, it was used to analyze the critical phenomena in the two dimensional statistical physics. Kac studied left \(L\)-modules, called the Verma modules, and obtained a formula for the determinants of the matrices of their vacuum expectation values. Feigin and Fuks used the formula to determine the composition series. In this note, another kind of representations of \(L\), called the Fock space representations, and intertwining operators between them are constructed. The analogous determinant formula for them is given.
scientific article; zbMATH DE number 3987519