Coulomb branches of quiver gauge theories with symmetrizers

Nakajima, Hiraku; Weekes, Alex

doi:10.48550/arxiv.1907.06552

Cited by 15 publications

(35 citation statements)

References 20 publications

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“…The isomorphisms (1.3) concern subcategories and already depend on the choice of Q-data (see Theorem 1.5 below). Also we note that our isomorphisms are not deduced from the results in [47,43].…”

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confidence: 88%

“…Note that in their recent study of the non-symmetric quantized Coulomb branches [47,43], Nakajima and Weekes established a parametrization of simple modules in nonsimply-laced types in terms of simple modules in simply-laced types and proved that q-characters of simple modules of non-symmetric Kac-Moody algebras are obtained from those of unfolded symmetric ones by imposing a certain modulus condition. In particular, they solved the character problem for simple modules by a different approach.…”

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confidence: 99%

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Isomorphisms among quantum Grothendieck rings and propagation of positivity

Fujita,

Hernandez,

et al. 2021

Preprint

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Let (g, g) be a pair of complex finite-dimensional simple Lie algebras whose Dynkin diagrams are related by (un)folding, with g being of simply-laced type. We construct a collection of ring isomorphisms between the quantum Grothendieck rings of monoidal categories Cg and Cg of finite-dimensional representations over the quantum loop algebras of g and g respectively. As a consequence, we solve longstanding problems : the positivity of the analogs of Kazhdan-Lusztig polynomials and the positivity of the structure constants of the quantum Grothendieck rings for any non-simply-laced g. In addition, comparing our isomorphisms with the categorical relations arising from the generalized quantum affine Schur-Weyl dualities, we prove the analog of Kazhdan-Lusztig conjecture (formulated in [17]) for simple modules in remarkable monoidal subcategories of Cg for any non-simply-laced g, and for any simple finite-dimensional modules in Cg for g of type Bn. In the course of the proof we obtain and combine several new ingredients. In particular we establish a quantum analog of T -systems, and also we generalize the isomorphisms of [24,26] to all g in a unified way, that is isomorphisms between subalgebras of the quantum group of g and subalgebras of the quantum Grothendieck ring of Cg.

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confidence: 88%

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confidence: 99%

Isomorphisms among quantum Grothendieck rings and propagation of positivity

Fujita,

Hernandez,

et al. 2021

Preprint

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“…Recently, Nakajima and Weekes have also generalized this to more general symmetrizable theories [44]. In particular, quiver folding allows one to get non-simply laced quivers from simply-laced ones.…”

Section: Question 3 Can We Find Any Relation Between Symplectic Duali...mentioning

confidence: 99%

Some Open Questions in Quiver Gauge Theory

Bao,

Hanany,

et al. 2021

Preprint

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Quivers, gauge theories and singular geometries are of great interest in both mathematics and physics. In this note, we collect a few open questions which have arisen in various recent works at the intersection between gauge theories, representation theory, and algebraic geometry. The questions originate from the study of supersymmetric gauge theories in different dimensions with different supersymmetries. Although these constitute merely the tip of a vast iceberg, we hope this guide can give a hint of possible directions in future research.This is an invited contribution to a special volume of Proyecciones, E. Gasparim, Ed., and it is the hope that the questions are specific enough for research projects aimed at PhD students.

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“…However, while all the ingredients of a simply laced Dynkin diagram -gauge and flavor nodes, hypermultiplet links -are readily interpretable, it was unknown at the time what to make of the novel multiple link. Recently [3] argued that their Coulomb branches result from a discrete folding operation on Coulomb branches of simply laced quivers. We independently derive and illustrate the same claim through the method of abelianisation [4].…”

Section: Introductionmentioning

confidence: 99%

“…Coulomb branches of balanced A 2n−1 -type quivers, ie. framed linear quivers satisfying the balance condition 3 and exhibiting sl(2n, C) symmetry on the Coulomb branch, can be "folded" into Coulomb branches of balanced C n -type quivers with usp(2n, C) symmetry. Balanced D n -type quiver Coulomb branches, ie.…”

Section: Introductionmentioning

confidence: 99%

Quiver origami: discrete gauging and folding

Bourget,

Hanany,

Miketa

2020

Preprint

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Coulomb branches of quiver gauge theories with symmetrizers

Cited by 15 publications

References 20 publications

Isomorphisms among quantum Grothendieck rings and propagation of positivity

Isomorphisms among quantum Grothendieck rings and propagation of positivity

Some Open Questions in Quiver Gauge Theory

Quiver origami: discrete gauging and folding

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