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### Jack symmetric functions and representations of the Virasoro algebra

**Algebra & Discrete Mathematics**

Speaker: | Reiho Sakamoto, Universito of Tokyo |

Location: | 1147 MSB |

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.