Vertex Algebras and Coordinate Rings of Semi-infinite Flags

  • Evgeny Feigin
  • Ievgen MakedonskyiEmail author


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.


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The work on Sections 1, 2, 3 was partially supported by the Russian Academic Excellence Project ‘5-100’. The work on Sections 4,5,6 was partially supported by the grant RSF-DFG 16-41-01013.


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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsNational Research University Higher School of EconomicsMoscowRussia
  2. 2.Department of MathematicsKyoto UniversityKyotoJapan

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