Jack symmetric functions and representations of the Virasoro algebraAlgebra & Discrete Mathematics
|Speaker:||Reiho Sakamoto, Universito of Tokyo|
|Start time:||Fri, Oct 6 2006, 12:10PM|
We use the Jack symmetric functions as a basis of the Fock space, and study the representation of the Virasoro algebra on this basis. As a result, we obtain a new combinatorial representation of the Virasoro algebra which intimately related to the singular vectors of the Fock space. We conjecture explicit form of the matrix elements of this representation. As a limiting case of these formulas, we obtain formulas for product of a power sum and a Jack symmetric function, and for differentiation of a Jack symmetric function by a power sum.
Reference: R.Sakamoto, J.Shiraishi, D.Arnaudon, L.Frappat, E.Ragoucy, Nucl.Phys.B704(2005)490-509.