The Deligne-Simpson Problem

2025/09/15 by Crawley-Boevey, William, Hubery, Andrew
#15A24 (Primary) 14H60 #16G20 #34M50 (Secondary) #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2509.11998

Abstract

Given k similarity classes of invertible matrices, the Deligne-Simpson problem asks to determine whether or not one can find matrices in these classes whose product is the identity and with no common invariant subspace. The first author conjectured an answer in terms of an associated root system, and proved one implication in joint work with Shaw. In this paper we prove the other implication, thus confirming the conjecture.

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Related

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