Galois coverings and the Clebsch-Gordan problem for quiver representations

• Autorzy: Martin Herschend
• Języki publikacji: EN

Abstrakty

EN

We study the Clebsch-Gordan problem for quiver representations, i.e. the problem of decomposing the point-wise tensor product of any two representations of a quiver into its indecomposable direct summands. For this purpose we develop results describing the behaviour of the point-wise tensor product under Galois coverings. These are applied to solve the Clebsch-Gordan problem for the double loop quivers with relations αβ = βα = αⁿ = βⁿ = 0. These quivers were originally studied by I. M. Gelfand and V. A. Ponomarev in their investigation of representations of the Lorentz group. We also solve the Clebsch-Gordan problem for all quivers of type 𝔸̃ₙ.

Kategorie tematyczne

• 47A80: Tensor products of operators
• 16G20: Representations of quivers and partially ordered sets

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2007
• Tom: 109
• Numer: 2
• Strony: 193-215

Daty

wydano

2007

Twórcy

autor

Martin Herschend

• Department of Mathematics, Uppsala University, Box 480, SE-751 06 Uppsala, Sweden

Identyfikatory

DOI

10.4064/cm109-2-3