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M. Finkelberg and E. Goncharov, Coulomb branch of a multiloop quiver gauge theory , 2019, arXiv: 1903.05822
Original
1903
Earlier work this paper cites.
by same author, Gelfand-Tsetlin modules in the Coulomb context , 2019, arXiv: 1904.05415
Original
1904
Earlier work this paper cites.
M. Demazure, Invariants symétriques entiers des groupes de Weyl et torsion , Invent. Math. 21
1973
Earlier work this paper cites.
H. Nakajima, Instantons on ALE spaces, quiver varieties, and Kac-Moody algebras , Duke Mathematical Journal 76
1994
Earlier work this paper cites.
W. Fulton, Intersection theory , 2 ed., Springer, 1998
1998
Earlier work this paper cites.
V. Mazorchuk, Orthogonal gelfand-zetlin algebras i , Beiträge zur Algebra und Geometrie 40
1999
Earlier work this paper cites.
M. Brion, Poincaré duality and equivariant (co)homology , Michigan Math. J. 48
2000
Earlier work this paper cites.
S. Kumar, Kac-Moody groups, their flag varieties and representation theory , Birkhäuser, 2002
2002
Earlier work this paper cites.
A. Gerasimov, S. Kharchev, D. Lebedev, and S. Oblezin, On a class of representations of the Yangian and moduli space of monopoles , Communications in Mathematical Physics 260
2005
Earlier work this paper cites.
T. Holm and R. Sjamaar, Torsion and Abelianization in equivariant cohomology , Transf. groups 13
2008
Earlier work this paper cites.
M. Khovanov, A. Lauda, M. Mackaay, and M. Stos̆ić, Extended graphical calculus for categorified quantum 𝔰 𝔩 2 \mathfrak{sl}_{2} , Mem. Am. Math. Soc. 219
2012
Earlier work this paper cites.
S. Cremonesi, A. Hanany, and A. Zaffaroni, Monopole operators and Hilbert series of Coulomb branches of 3 d 3d 𝒩 = 4 \mathcal{N}=4 gauge theories , JHEP 1401
2014
Earlier work this paper cites.
M. Finkelberg and L. Rybnikov, Quantization of Drinfeld Zastava in type A , Journal of the European Mathematical Society 16
2014
Earlier work this paper cites.
by same author, Quantization of Drinfeld Zastava in type C , Algebraic Geometry 1
2014
Earlier work this paper cites.

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J. Kamnitzer, B. Webster, A. Weekes, and O. Yacobi, Yangians and quantization of slices in the affine Grassmannian , Algebra and Number Theory 8
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Then

G. Lonergan, Steenrod operations, the Coulomb branch and the Frobenius twist, I , 2017, arXiv: 1712.03711
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Later among the works it cites.
S. Cautis and H. Williams, Cluster theory of the coherent Satake category , 2018, arXiv: 1801.08111
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Later among the works it cites.
M. Finkelberg, J. Kamnitzer, K. Pham, L. Rybnikov, and A. Weekes, Comultiplication for shifted Yangians and quantum open Toda lattice , Advances in Mathematics (2018), 349–389
2018
Later among the works it cites.
by same author, Shifted quantum affine algebras: integral forms in type A A (with appendices by A. Tsymbaliuk and A. Weekes) , 2018, arXiv: 1811.12137
Original
2018
Later among the works it cites.
V. Ginzburg, Nil-Hecke algebras and Whittaker 𝒟 \mathscr{D} –modules , in Lie groups, Geometry, and Representation Theory, Prog. Math. 326

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2019

Generators for Coulomb branches of quiver gauge theories

Weekes, Alex

Understand

We study the Coulomb branches of $3d$ $\mathcal{N}=4$ quiver gauge theories, focusing on the generators for their quantized coordinate rings.

We show that there is a surjective map from a shifted Yangian onto the quantized Coulomb branch, once the deformation parameter is set to $\hbar =1$.
In finite ADE type, this extends to a surjection over $\mathbb{C}[\hbar]$.
We also show that these algebras are generated by the dressed minuscule monopole operators, for an arbitrary quiver (this is similar to the proof of Theorem 4.29 in arXiv:1811.12137).

Built on

M. Finkelberg and E. Goncharov, Coulomb branch of a multiloop quiver gauge theory , 2019, arXiv: 1903.05822
Original
1903
Earlier work this paper cites.
by same author, Gelfand-Tsetlin modules in the Coulomb context , 2019, arXiv: 1904.05415
Original
1904
Earlier work this paper cites.
M. Demazure, Invariants symétriques entiers des groupes de Weyl et torsion , Invent. Math. 21
1973
Earlier work this paper cites.
H. Nakajima, Instantons on ALE spaces, quiver varieties, and Kac-Moody algebras , Duke Mathematical Journal 76
1994
Earlier work this paper cites.
W. Fulton, Intersection theory , 2 ed., Springer, 1998
1998
Earlier work this paper cites.
V. Mazorchuk, Orthogonal gelfand-zetlin algebras i , Beiträge zur Algebra und Geometrie 40
1999
Earlier work this paper cites.
M. Brion, Poincaré duality and equivariant (co)homology , Michigan Math. J. 48
2000
Earlier work this paper cites.
S. Kumar, Kac-Moody groups, their flag varieties and representation theory , Birkhäuser, 2002
2002
Earlier work this paper cites.
A. Gerasimov, S. Kharchev, D. Lebedev, and S. Oblezin, On a class of representations of the Yangian and moduli space of monopoles , Communications in Mathematical Physics 260
2005
Earlier work this paper cites.
T. Holm and R. Sjamaar, Torsion and Abelianization in equivariant cohomology , Transf. groups 13
2008
Earlier work this paper cites.
M. Khovanov, A. Lauda, M. Mackaay, and M. Stos̆ić, Extended graphical calculus for categorified quantum 𝔰 𝔩 2 \mathfrak{sl}_{2} , Mem. Am. Math. Soc. 219
2012
Earlier work this paper cites.
S. Cremonesi, A. Hanany, and A. Zaffaroni, Monopole operators and Hilbert series of Coulomb branches of 3 d 3d 𝒩 = 4 \mathcal{N}=4 gauge theories , JHEP 1401
2014
Earlier work this paper cites.
M. Finkelberg and L. Rybnikov, Quantization of Drinfeld Zastava in type A , Journal of the European Mathematical Society 16
2014
Earlier work this paper cites.
by same author, Quantization of Drinfeld Zastava in type C , Algebraic Geometry 1
2014
Earlier work this paper cites.

Similar

J. Kamnitzer, B. Webster, A. Weekes, and O. Yacobi, Yangians and quantization of slices in the affine Grassmannian , Algebra and Number Theory 8
2014
Cited alongside, same era.
by same author, Towards a mathematical definition of Coulomb branches of 3-dimensional 𝒩 = 4 \mathcal{N}=4 gauge theories, I , 2015, arXiv: 1503.03676
Original
2015
Cited alongside, same era.
M. Bullimore, T. Dimofte, D. Gaiotto, and J. Hilburn, Boundaries, mirror symmetry, and symplectic duality in 3 d 3d 𝒩 = 4 \mathcal{N}=4 gauge theory , JHEP 10
2016
Cited alongside, same era.
A. Braverman, P. Etingof, and M. Finkelberg, Cyclotomic double affine Hecke algebras , 2016, arXiv: 1611.10216
Original
2016
Cited alongside, same era.
A. Braverman, M. Finkelberg, and H. Nakajima, Coulomb branches of 3 d 3d 𝒩 = 4 \mathcal{N}=4 quiver gauge theories and slices in the affine Grassmannian (with appendices by A. Braverman, M. Finkelberg, J. Kamnitzer, R. Kodera, H. Nakajima, B. Webster, and A. Weekes) , 2016, arXiv: 1604.03625

Then

G. Lonergan, Steenrod operations, the Coulomb branch and the Frobenius twist, I , 2017, arXiv: 1712.03711
Original
2017
Later among the works it cites.
S. Cautis and H. Williams, Cluster theory of the coherent Satake category , 2018, arXiv: 1801.08111
Original
2018
Later among the works it cites.
M. Finkelberg, J. Kamnitzer, K. Pham, L. Rybnikov, and A. Weekes, Comultiplication for shifted Yangians and quantum open Toda lattice , Advances in Mathematics (2018), 349–389
2018
Later among the works it cites.
by same author, Shifted quantum affine algebras: integral forms in type A A (with appendices by A. Tsymbaliuk and A. Weekes) , 2018, arXiv: 1811.12137
Original
2018
Later among the works it cites.
V. Ginzburg, Nil-Hecke algebras and Whittaker 𝒟 \mathscr{D} –modules , in Lie groups, Geometry, and Representation Theory, Prog. Math. 326

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

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