Vertex algebras and coordinate rings of semi-infinite flags

Date
2018/04/19 Thu 10:30 - 12:00
Speaker
Ievgen Makedonskyi
Affiliation
Kyoto U.
Abstract

The direct sum of irreducible level one integrable representations
of affne Kac-Moody Lie algebra of (affne) type ADE carries
a structure of P/Q-graded vertex operator algebra. There exists a fi ltration
on these modules due to Kato and Loktev such that the corresponding
graded vector space is a direct sum of global Weyl modules.
The associated graded space with respect to the dual filtration is isomorphic
to the homogenous coordinate ring of semi-in finite flag variety.
We describe the ring structure in terms of vertex operators and endow
the homogenous coordinate ring with a structure of P/Q-graded vertex
operator algebra. We use the vertex algebra approach to derive semiinfi nite
Pluecker-type relations in the homogeneous coordinate ring.

(The seminar will be hold at RIMS room 006.)