Galois coverings and the Clebsch-Gordan problem for quiver representations

Martin Herschend. "Galois coverings and the Clebsch-Gordan problem for quiver representations." Colloquium Mathematicae 109.2 (2007): 193-215. <http://eudml.org/doc/286491>.

@article{MartinHerschend2007,
abstract = {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.},
author = {Martin Herschend},
journal = {Colloquium Mathematicae},
keywords = {quiver representations; tensor products; Clebsch-Gordan problem; Galois coverings; extended Dynkin quivers; representation rings; indecomposable direct summands},
language = {eng},
number = {2},
pages = {193-215},
title = {Galois coverings and the Clebsch-Gordan problem for quiver representations},
url = {http://eudml.org/doc/286491},
volume = {109},
year = {2007},
}

TY - JOUR
AU - Martin Herschend
TI - Galois coverings and the Clebsch-Gordan problem for quiver representations
JO - Colloquium Mathematicae
PY - 2007
VL - 109
IS - 2
SP - 193
EP - 215
AB - 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.
LA - eng
KW - quiver representations; tensor products; Clebsch-Gordan problem; Galois coverings; extended Dynkin quivers; representation rings; indecomposable direct summands
UR - http://eudml.org/doc/286491
ER -