Unitarizable representations of quivers

Details Unitarizable representations of quivers Unitarizable representations of quivers

2010-12-28

arxiv.org/abs/1012.5777v3

Mathematics

Representation Theory

25 pages, paper reorganized

Scientific paper

We investigate representations of *-algebras associated with posets. Unitarizable representations of the corresponding (bound) quivers (which are polystable representations for some appropriately chosen slope function) give rise to representations of these algebras. If the poset corresponds to an unbound quiver this leads to an ADE-classification which describes the unitarization behaviour of its representations. If the poset corresponds to a bound quiver, it is possible to construct unitarizable representations starting with polystable representations of a related unbound quiver which can be glued together with a suitable direct sum of simple representations. Finally, we estimate the number of complex parameters parametrizing irreducible unitary non-equivalent representations of the corresponding algebras.

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