Vertex Algebras and Coordinate Rings of Semi-infinite Flags

Evgeny Feigin, Ievgen Makedonskyi

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

The direct sum of irreducible level one integrable representations of affine Kac-Moody Lie algebra of (affine) type ADE carries a structure of P/Q-graded vertex operator algebra. There exists a filtration on this direct sum studied by 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-infinite 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 semi-infinite Plücker-type relations in the homogeneous coordinate ring.

Original languageEnglish
Pages (from-to)221-244
Number of pages24
JournalCommunications in Mathematical Physics
Volume369
Issue number1
DOIs
Publication statusPublished - 1 Jul 2019
Externally publishedYes

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