A Weyl Module Stratification of Integrable Representations

Kato, Syu; Loktev, S.

doi:10.1007/s00220-019-03327-5

Cited by 3 publications

(1 citation statement)

References 43 publications

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“…The current algebra g ⊗ C[t] can be seen as an intermediate step between g and g. In particular, its representation theory (algebraic, geometric and combinatorial) has various deep connections with representation theory of g and that of g (see e.g. [CL,FL,FM1,KL]). The current algebra has two important classes of cyclic representations: local Weyl modules W λ and global Weyl modules W λ ( [CP, CFK, FMO]).…”

Section: Introductionmentioning

confidence: 99%

Vertex Algebras and Coordinate Rings of Semi-infinite Flags

Feigin

Makedonskyi

2019

Commun. Math. Phys.

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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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Section: Introductionmentioning

confidence: 99%

Vertex Algebras and Coordinate Rings of Semi-infinite Flags

Feigin

Makedonskyi

2019

Commun. Math. Phys.

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Nonsymmetric Rogers-Ramanujan sums and thick Demazure modules

Cherednik

Kato

2020

Advances in Mathematics

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Frobenius splitting of Schubert varieties of semi-infinite flag manifolds

Kato

2021

Forum of Mathematics, Pi

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We exhibit basic algebro-geometric results on the formal model of semi-infinite flag varieties and its Schubert varieties over an algebraically closed field ${\mathbb K}$ of characteristic $\neq 2$ from scratch. We show that the formal model of a semi-infinite flag variety admits a unique nice (ind-)scheme structure, its projective coordinate ring has a $\mathbb {Z}$ -model and it admits a Frobenius splitting compatible with the boundaries and opposite cells in positive characteristic. This establishes the normality of the Schubert varieties of the quasi-map space with a fixed degree (instead of their limits proved in [K, Math. Ann. 371 no.2 (2018)]) when $\mathsf {char}\, {\mathbb K} =0$ or $\gg 0$ , and the higher-cohomology vanishing of their nef line bundles in arbitrary characteristic $\neq 2$ . Some particular cases of these results play crucial roles in our proof [47] of a conjecture by Lam, Li, Mihalcea and Shimozono [60] that describes an isomorphism between affine and quantum K-groups of a flag manifold.

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A Weyl Module Stratification of Integrable Representations

Cited by 3 publications

References 43 publications

Vertex Algebras and Coordinate Rings of Semi-infinite Flags

Vertex Algebras and Coordinate Rings of Semi-infinite Flags

Nonsymmetric Rogers-Ramanujan sums and thick Demazure modules

Frobenius splitting of Schubert varieties of semi-infinite flag manifolds

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