Geodesic
On the primality of totally ordered q-factorization graphs
Canadian journal of mathematics, Tome 76 (2024) no. 2, pp. 594-637

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DOI

We introduce the combinatorial notion of a q-factorization graph intended as a tool to study and express results related to the classification of prime simple modules for quantum affine algebras. These are directed graphs equipped with three decorations: a coloring and a weight map on vertices, and an exponent map on arrows (the exponent map can be seen as a weight map on arrows). Such graphs do not contain oriented cycles and, hence, the set of arrows induces a partial order on the set of vertices. In this first paper on the topic, beside setting the theoretical base of the concept, we establish several criteria for deciding whether or not a tensor product of two simple modules is a highest-$\ell $-weight module and use such criteria to prove, for type A, that a simple module whose q-factorization graph has a totally ordered vertex set is prime.
DOI : 10.4153/S0008414X23000160
Mots-clés : Quantum affine algebras, representation theory, tensor product factorization, simple prime modules 
Moura, Adriano; Silva, Clayton. On the primality of totally ordered q-factorization graphs. Canadian journal of mathematics, Tome 76 (2024) no. 2, pp. 594-637. doi: 10.4153/S0008414X23000160
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