Proof of the tree module property for exceptional representations of the quiver 𝔼_6

12/31/2019

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by   Szabolcs Lénárt, et al.

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This document (together with the ancillary file e6_proof.pdf) is an appendix to the paper [12]. The ancillary file contains the computer generated part of the proof of the main result in [12], giving a complete and general list of tree representations corresponding to exceptional modules over the path algebra of the canonically oriented Euclidean quiver 𝔼_6. The proof (involving induction and symbolic computation with block matrices) was partially generated by a purposefully developed computer software, outputting in a detailed step-by-step fashion as if written "by hand". Tree representations are exhibited using matrices involving only the elements 0 and 1, and all representations enlisted in the ancillary document remain valid over any base field.