Vertex Algebras at the Corner

Gaiotto, Davide; Rapčák, Miroslav

doi:10.48550/arxiv.1703.00982

Cited by 26 publications

(113 citation statements)

References 46 publications

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“…The quotient of U q ( gl 1 ) by the two-sided ideal generated by operators, which act as 0 on any such tensor product is a certain W algebra depending on three integer parameters k, n, m. These algebras (or, rather, their conformal limits) appear recently in [31], [22] in a different context, the formulas for screening operators for these algebras follows from the Lemmas 5.1, 5.2. We hope to study these algebras in more details elsewhere.…”

Section: Now We Want To Consider Tensor Productsmentioning

confidence: 99%

Plane partitions with a “pit”: generating functions and representation theory

Bershtein

Feigin

Merzon

2018

Sel. Math. New Ser.

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We study plane partitions satisfying condition a n+1,m+1 = 0 (this condition is called "pit") and asymptotic conditions along three coordinate axes. We find the formulas for generating function of such plane partitions.Such plane partitions label the basis vectors in certain representations of quantum toroidal gl 1 algebra, therefore our formulas can be interpreted as the characters of these representations. The resulting formulas resemble formulas for characters of tensor representations of Lie superalgebra gl m|n . We discuss representation theoretic interpretation of our formulas using q-deformed W -algebra gl m|n .1 Usually a formula is called bosonic if it equals a linear combination of characters of algebra of polynomials. In our case bosonic formula is a combination of terms q ∆ /(q) n+m ∞ .

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Section: Now We Want To Consider Tensor Productsmentioning

confidence: 99%

Plane partitions with a “pit”: generating functions and representation theory

Bershtein

Feigin

Merzon

2018

Sel. Math. New Ser.

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“…Spiked instantons admit a presentation in terms of framed quiver representations of a triply framed generalization of the ADHM quiver labelled by framing vectors (r 1 , r 2 , r 3 ) ∈ (Z ≥0 ) ×3 . It was shown in [RSYZ18] that the dual of the compactly supported equivariant vanishing cycle cohomology of moduli spaces of stable framed representations with fixed (r 1 , r 2 , r 3 ) carries an action of the vertex algebra V r1,r2,r3 introduced in [GR19]. Moreover, the resulting module is identified with a Verma module with the highest weight depending on the equivariant parameters.…”

Section: Further Remarks and Open Directionsmentioning

confidence: 99%

“…Finally, motivated by work of Gaiotto and Rapcak [GR19], Nekrasov [Nek17] and Nekrasov and Prabhakar [NP17], an action of a more general class of vertex algebras on the dual of the compactly supported equivariant vanishing cycle cohomology of certain quiver moduli spaces was constructed by Rapcak, Soibelman, Yang and Zhao in [RSYZ18].…”

Section: Introductionmentioning

confidence: 99%

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Hilbert schemes of nonreduced divisors in Calabi-Yau threefolds and W-algebras

Chuang

Creutzig

Diaconescu

et al. 2019

Preprint

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A W -algebra action is constructed on the equivariant Borel-Moore homology of the Hilbert scheme of points on a nonreduced plane in three dimensional affine space, identifying it to the vacuum W -module. This is based on a generalization of the ADHM construction as well as the W -action on the equivariant Borel-Moore homology of the moduli space of instantons constructed by Schiffmann and Vasserot.

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“…It would be intriguing to study such pairs of W-algebras corresponding to the Rigid SCFTs among T ρ [G]. It would also be interesting to compare this with other associations between 3d N 4 SCFTs and Vertex Operator Algebras [97,98].…”

Section: Mass Deformations and The Local Agt Correspondencementioning

confidence: 99%

Masses, Sheets and Rigid SCFTs

Balasubramanian¹,

Distler²

2018

Preprint

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We study mass deformations of certain three dimensional N 4 Superconformal Field Theories (SCFTs) that have come to be called T ρ [G] theories. These are associated to tame defects of the six dimensional (0, 2) SCFT X[j] for j A, D, E. We describe these deformations using a refined version of the theory of sheets, a subject of interest in Geometric Representation Theory. In mathematical terms, we parameterize local mass-like deformations of the tamely ramified Hitchin integrable system and identify the subset of the deformations that do admit an interpretation as a mass deformation for the theories under consideration. We point out the existence of non-trivial Rigid SCFTs among these theories. We classify the Rigid theories within this set of SCFTs and give a description of their Higgs and Coulomb branches. We then study the implications for the endpoints of RG flows triggered by mass deformations in these 3d N 4 theories. Finally, we discuss connections with the recently proposed idea of Symplectic Duality and describe some conjectures about its action.

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Vertex Algebras at the Corner

Cited by 26 publications

References 46 publications

Plane partitions with a “pit”: generating functions and representation theory

Plane partitions with a “pit”: generating functions and representation theory

Hilbert schemes of nonreduced divisors in Calabi-Yau threefolds and W-algebras

Masses, Sheets and Rigid SCFTs

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