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arXiv · 1804.03359

Vertex algebras and coordinate rings of semi-infinite flags

Evgeny Feigin·Ievgen Makedonskyi
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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 Pl\"ucker-type relations in the homogeneous coordinate ring.

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BibTeXRIS

Evgeny Feigin, Ievgen Makedonskyi. 2018-04-10. Vertex algebras and coordinate rings of semi-infinite flags. https://doi.org/10.1007/s00220-019-03321-x

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