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DOUBLE AFFINE GRASSMANNIANS AND COULOMB BRANCHES OF 3dN = 4 QUIVER GAUGE THEORIES
P. 1279–1298.
We propose a conjectural construction of various slices for double affine Grass-
mannians as Coulomb branches of 3-dimensional N = 4 supersymmetric affine quiver
gauge theories. It generalizes the known construction for the usual affine Grassman-
nians, and makes sense for arbitrary symmetric Kac-Mody algebras.
In book
World Scientific Publishing Co. Pte. Ltd, 2019.
Braverman A., Etingof P., Michael Finkelberg, Annales Scientifiques de l'Ecole Normale Superieure 2020 Vol. 53 No. 5 P. 1249–1312
We show that the partially spherical cyclotomic rational Cherednik algebra (obtained from the full rational Cherednik algebra by averaging out the cyclotomic part of the underlying
reflection group) has four other descriptions: (1) as a subalgebra of the degenerate DAHA of type A
given by generators; (2) as an algebra given by generators and relations; (3) as ...
Added: December 8, 2020
Гончаров Е. А., Finkelberg M. V., Функциональный анализ и его приложения 2019 Т. 53 № 4 С. 3–13
We compute the Coulomb branch of a multiloop quiver gauge theory for the quiver with a single vertex,
r loops, one-dimensional framing, and dim V = 2. We identify it with a Slodowy slice in the nilpotent cone of the
symplectic Lie algebra of rank r. Hence it possesses a symplectic resolution with 2r fixed points with respect ...
Added: November 28, 2019
Michael Finkelberg, Tsymbaliuk A., Arnold Mathematical Journal 2019 Vol. 5 No. 2-3 P. 197–283
We define an integral form of shifted quantum affine algebras of type A and construct
Poincaré–Birkhoff–Witt–Drinfeld bases for them. When the shift is trivial, our integral
form coincides with the RTT integral form. We prove that these integral forms are
closed with respect to the coproduct and shift homomorphisms. We prove that the
homomorphism from our integral form to ...
Added: November 14, 2019
Braverman A., Michael Finkelberg, Nakajima H., Advances in Theoretical and Mathematical Physics 2019 Vol. 23 No. 2 P. 253–344
We consider the
morphism from the variety of triples introduced in our previous paper to the
affine Grassmannian. The direct image of the dualizing complex is a
ring object in the equivariant derived category on the affine Grassmannian (equivariant derived Satake category). We show that various constructions in our previous paper work for an arbitrary commutative
ring object.
The second purpose of this ...
Added: November 12, 2019
Braverman A., Michael Finkelberg, Nakajima H., Advances in Theoretical and Mathematical Physics 2019 Vol. 23 No. 1 P. 75–166
This is a companion paper of [Part II]. We study Coulomb branches
of unframed and framed quiver gauge theories of type ADE. In the
unframed case they are isomorphic to the moduli space of based rational maps from P^1 to the flag variety. In the framed case they are
slices in the affine Grassmannian and their generalization. In ...
Added: September 28, 2019
Finkelberg M. V., Goncharov E., / Series arXiv "math". 2019.
We compute the Coulomb branch of a multiloop quiver gauge theory for the quiver with a single vertex, r loops, one-dimensional framing, and dim V = 2. We identify it with a Slodowy slice in the nilpotent cone of the symplectic Lie algebra of rank r. Hence it possesses a symplectic resolution with 2r fixed points with respect to a Hamiltonian ...
Added: June 9, 2019
Braverman A., Michael Finkelberg, Nakajima H., Advances in Theoretical and Mathematical Physics 2018 Vol. 22 No. 5 P. 1071–1147
Consider the 3-dimensional N = 4 supersymmetric gauge theory associated with a compact Lie group Gc and its quaternionic representation M. Physicists study its Coulomb branch, which is a noncompact hyper-K¨ahler manifold with an SU(2)-action, possibly with singularities. We give a mathematical definition of the Coulomb branch as an affine algebraic variety with C×-action when ...
Added: May 3, 2019
Finkelberg M. V., Kubrak D., Functional Analysis and Its Applications 2015 Vol. 49 No. 2 P. 135–141
We slightly extend results of Evens and Mirković and “compute” the characteristic cycles of intersection cohomology sheaves on transversal slices in a double affine Grassmannian. We propose a conjecture relating the hyperbolic stalks and microlocalization at a torus-fixed point in a Poisson variety. © 2015, Springer Science+Business Media New York. ...
Added: September 3, 2015
Kubrak D., Finkelberg M. V., Функциональный анализ и его приложения 2015 Т. 49 № 2 С. 70–78
Мы немного обобщаем результаты Мирковича-Эванса и вычисляем характеристические циклы пучков Горески-Макферсона на трансверсальных срезах в двойном аффинном грассманниане. Мы также выдвигаем гипотезу, связывающую гиперболические слои и микролокализацию в неподвижной относительно действия тора точке пуассонова многообразия. ...
Added: June 12, 2015
Finkelberg M. V., Braverman A., Advances in Mathematics 2012 No. 230 P. 414–432
This is the second paper of the series, started by Braverman-Finkelberg (2010) which describes a conjectural analogue of the affine Grassmannian for affine Kac-Moody groups (also known as double affine Grassmannian). The current paper is dedicated to describing a conjectural analogue of the convolution diagram for the double affine Grassmannian. In case our group is ...
Added: December 3, 2012