Rational quiver representations: tame and wild

2025/10/01 by Januszewski, Fabian
#16G20 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2510.00924

Abstract

We study representation finite K-rational quivers over fields of characteristic 0 and their indecomposable representations, exploiting that all Brauer obstructions for descent of representations are trivial in this case. Contrasting the tame case, we give an example of a simple quiver of wild representation type, where we realize every possible Brauer obstruction of a given Galois extension L/K in the category of quiver representations over L.

Citations

• Rational structures on quivers and a generalization of Gelfand's equivalence
• Locally algebraic representations and integral structures on the cohomology of arithmetic groups
• On Period Relations for Automorphic L-functions I
• Rational Structures on Automorphic Representations
• Unzerlegbare Darstellungen I

Related

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• Rational structures on quivers and a generalization of Gelfand's equivalence
• On complexity of representations of quivers
• The representations of quivers of type A_n. A fast approach
• Counting Representations of Quivers Respecting Nilpotent Relations over Finite Fields