Reality determining subgraphs and strongly real modules
Abstract
The concept of pseudo q-factorization graphs was recently introduced by the last two authors as a combinatorial language which is suited for capturing certain properties of Drinfeld polynomials. Using certain known representation theoretic facts about tensor products of Kirillov Reshetikhin modules and qcharacters, combined with special topological/combinatorial properties of the underlying q-factorization graphs, the last two authors showed that, for algebras of type A, modules associated to totally ordered graphs are prime, while those associated to trees are real. In this paper, we extend the latter result. We introduce the notions of strongly real modules and that of trees of modules satisfying certain properties. In particular, we can consider snake trees, i.e., trees formed from snake modules. Among other results, we show that a certain class of such generalized trees, which properly contains the snake trees, give rise to strongly real modules.
Cite
@article{arxiv.2406.06970,
title = {Reality determining subgraphs and strongly real modules},
author = {Matheus Brito and Adriano Moura and Clayton Silva},
journal= {arXiv preprint arXiv:2406.06970},
year = {2025}
}
Comments
This is the version which was accepted for publication by J. Alg. and contains corrections and additions suggested by the referee as well as a corrected link to one of the references