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Coulomb Branch of a Multiloop Quiver

Student: Evgeny Goncharov

Supervisor: Mikhail V. Finkelberg

Faculty: Faculty of Mathematics

Educational Programme: Mathematics (Bachelor)

Final Grade: 10

Year of Graduation: 2019

We compute the Coulomb branch of a quiver with 1 vertex and l loops for dim V =2, dim W = 1 that turns out to be a hypersurface in the 5-dimensional affine space. If l = 1, it is just the second symmetric power of an affine plane which has a symplectic resolution given by the Hilbert scheme. We will construct the symplectic resolution in the general case by proving that the Coulomb branch for l greater or equal to 2 is isomorphic to the Slodowy slice to the subsubregular orbit in the symplectic Lie algebra of rank l corresponding to the Jordan partition (2l - 2, 1, 1). We will also show that there is no similar isomorphism for dim V =3, dim W = 1.

Full text (added May 1, 2019)

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