Unitary and Euclidean representations of a quiver

Details Unitary and Euclidean representations of a quiver Unitary and Euclidean representations of a quiver

2007-09-15

arxiv.org/abs/0709.2444v1

Linear Algebra Appl. 278 (1998) 37-62

Mathematics

Representation Theory

Scientific paper

10.1016/S0024-3795(98)00006-8

A unitary (Euclidean) representation of a quiver is given by assigning to each vertex a unitary (Euclidean) vector space and to each arrow a linear mapping of the corresponding vector spaces. We recall an algorithm for reducing the matrices of a unitary representation to canonical form, give a certain description of the representations in canonical form, and reduce the problem of classifying Euclidean representations to the problem of classifying unitary representations. We also describe the set of dimensions of all indecomposable unitary (Euclidean) representations of a quiver and establish the number of parameters in an indecomposable unitary representation of a given dimension.

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