Canonically Jordan recoverable categories for modules over the path algebra of A_n type quivers

2023/08/31 by Dequêne, Benjamin
#Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2308.16626

Abstract

Let Q be a quiver of A_n type and \mathbbK be an algebraically closed field. A nilpotent endomorphism of a quiver representation induces a linear transformation of the vector space at each vertex. Generically among all nilpotent endomorphisms of a fixed representation X, there exists a well-defined Jordan form of each of these linear transformations GenJF(X), called the generic Jordan form data of X. A subcategory of rep(Q) is Jordan recoverable if we can recover X up to isomorphism from its generic Jordan form data. There is a procedure which allows one to invert the map from representations to generic Jordan form data. The subcategories for which this procedure works are called canonically Jordan recoverable. We focus on the subcategories of rep(Q) that are canonically Jordan recoverable, and we give a combinatorial characterization of them.

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