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June 2018 Automorphisms of order three of the moduli space of Spin-Higgs bundles
Álvaro Antón SANCHO
Hokkaido Math. J. 47(2): 387-426 (June 2018). DOI: 10.14492/hokmj/1529308825

Abstract

In this work we consider a family of ${\rm Spin}$ complex groups constructed in \cite{anton-article} which have outer automorphisms of order three. We define an action of ${\rm Out}({\rm Spin}(n,\mathbb{C}))\times\mathbb{C}^*$ on the moduli space of ${\rm Spin}$-Higgs bundles and we study the subvariety of fixed points of the induced automorphisms of order three. These fixed points can be expressed in terms of some kind of Higgs pairs associated to certain subgroups of ${\rm Spin}(n,\mathbb{C})$ equipped with a representation of the subgroup. We further the study for the simple case, $G={\rm Spin}(8,\mathbb{C})$.

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Álvaro Antón SANCHO. "Automorphisms of order three of the moduli space of Spin-Higgs bundles." Hokkaido Math. J. 47 (2) 387 - 426, June 2018. https://doi.org/10.14492/hokmj/1529308825

Information

Published: June 2018
First available in Project Euclid: 18 June 2018

zbMATH: 06901712
MathSciNet: MR3815299
Digital Object Identifier: 10.14492/hokmj/1529308825

Subjects:
Primary: 14D20

Keywords: ${\rm Spin}$-Higgs bundles , Fixed points , Higgs pair , moduli space , triality

Rights: Copyright © 2018 Hokkaido University, Department of Mathematics

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Vol.47 • No. 2 • June 2018
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