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Stable representations of posets |
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| Institution: | 1. Department of Mathematics, Univ. of São Paulo, Caixa Postal 66281, São Paulo, SP 05315-970, Brazil;2. Department of Mathematics, University of California, Riverside, CA 92521, United States;3. Department of Mathematics, Rutgers University, Piscataway, NJ 08854, United States;1. School of Mathematics and Big Data, Foshan University, Guangdong, 528000, PR China;2. Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq;3. Department of Mathematics and Informatics, University of Novi Sad, Trg Dositeja Obradovi?a 4, 21101 Novi Sad, Serbia;4. Centre for Research in Mathematics, School of Computing, Engineering and Mathematics, Western Sydney University, Locked Bag 1797, Penrith, NSW 2751, Australia;5. Department of Mathematics, University of York, Heslington, York YO10 5DD, UK |
| Abstract: | The purpose of this paper is to study stable representations of partially ordered sets (posets) and compare it to the well known theory for quivers. In particular, we prove that every indecomposable representation of a poset of finite type is stable with respect to some weight and construct that weight explicitly in terms of the dimension vector. We show that if a poset is primitive then Coxeter transformations preserve stable representations. When the base field is the field of complex numbers we establish the connection between the polystable representations and the unitary χ-representations of posets. This connection explains the similarity of the results obtained in the series of papers. |
| Keywords: | Representations Posets Stability Coxeter transformations Moment map |
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