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Journal of Lie Theory 32 (2022), No. 3, 797--812
Copyright Heldermann Verlag 2022

Momentum Map Images of Representation Spaces of Quivers

Maria Bertozzi
Fakultät für Mathematik, Ruhr Universität, Bochum, Germany

Markus Reineke
Fakultät für Mathematik, Ruhr Universität, Bochum, Germany

We consider the base change action on real or complex representation spaces of quivers and the associated momentum map for a maximal compact subgroup of the base change group, as introduced by A. King. We give an explicit description of the momentum map image in terms of recursively defined inequalities on eigenvalues of Hermitian operators. Moreover, we characterize when the momentum map image is maximal possible, respectively of positive volume.

Keywords: Momentum map image, quiver, Hermitian operator.

MSC: 15A42, 16G20, 53D20.

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