The (cyclic) enhanced nilpotent cone via quiver representations

Bellamy, G. and Boos, M. (2018) The (cyclic) enhanced nilpotent cone via quiver representations. Manuscripta Mathematica, (doi:10.1007/s00229-018-1098-9) (Early Online Publication)

Bellamy, G. and Boos, M. (2018) The (cyclic) enhanced nilpotent cone via quiver representations. Manuscripta Mathematica, (doi:10.1007/s00229-018-1098-9) (Early Online Publication)

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Abstract

The GL(V )-orbits in the enhanced nilpotent cone V × N are (essentially) in bijection with the orbits of a certain parabolic P ⊆ GL(V ) (the mirabolic subgroup) in the nilpotent cone N. We give a new parameterization of the orbits in the enhanced nilpotent cone, in terms of representations of the underlying quiver. This parameterization generalizes naturally to the enhanced cyclic nilpotent cone. Our parameterizations are different from the previous ones that have appeared in the literature. Explicit translations between the different parametrizations are given.

Item Type:Articles
Status:Early Online Publication
Refereed:Yes
Glasgow Author(s) Enlighten ID:Bellamy, Dr Gwyn
Authors: Bellamy, G., and Boos, M.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Manuscripta Mathematica
Publisher:Springer
ISSN:0025-2611
ISSN (Online):1432-1785
Published Online:17 December 2018
Copyright Holders:Copyright © 2018 The Authors
First Published:First published in Manuscripta Mathematica 2018
Publisher Policy:Reproduced under a Creative Commons License

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
662571Symplectic representation theoryGwyn BellamyEngineering and Physical Sciences Research Council (EPSRC)EP/N005058/1M&S - MATHEMATICS