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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 |
Description
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.