Vertex algebras and coordinate rings of semi-infinite flags

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.

References in corpus (9)

• Vertex Algebras and Algebraic Curves
• BGG reciprocity for current algebras
• Abelianizing vertex algebras
• Generalized Vertex Algebras
• Semi-infinite Schubert varieties and quantum K-theory of flag manifolds
• Demazure character formula for semi-infinite flag varieties
• Weyl modules and q-Whittaker functions
• A Weyl Module Stratification of Integrable Representations (with an appendix by Ryosuke Kodera)
• Nonsymmetric Rogers-Ramanujan sums and thick Demazure modules

Cited by in corpus (5)

• Reduced arc schemes for Veronese embeddings and global Demazure modules
• Frobenius splitting of Schubert varieties of semi-infinite flag manifolds
• Beilinson-Drinfeld Schubert varieties and global Demazure modules
• Beilinson-Drinfeld Schubert varieties of parahoric group schemes and twisted global Demazure modules
• On reduced arc spaces of toric varieties