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Group actions on quiver varieties and application to branes

Posted in
Victoria Hoskins
Humboldt Universität Berlin
Tue, 28/11/2017 - 16:30 - 17:30
MPIM Lecture Hall

We study two types of actions on King's moduli spaces of quiver representations over a
field $k$, and we decompose their fixed loci using group cohomology in order to give
modular interpretations of the components. The first type of action arises by considering
finite groups of quiver automorphisms. The second is the absolute Galois group of a
perfect field $k$ acting on the points of this quiver moduli space valued in an algebraic
closure of $k$; the fixed locus is the set of $k$-rational points, which we decompose
using the Brauer group of $k$, and we describe the rational points as quiver representations
over central division algebras over $k$. Over the field of complex numbers, we describe the
symplectic and holomorphic geometry of these fixed loci in hyperk\"ahler quiver varieties
using the language of branes. This is joint work with Florent Schaffhauser.

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