sl3-Analogues of Infinite Dynkin Diagrams in Lie Representation Theory
The combinatorics of how the monoidal category of finite-dimensional sl3-modules acts on simple sl3-modules is captured by a finite family of exactly eight infinite oriented graphs, generalizing the way classical infinite Dynkin diagrams encode sl2-symmetries. Each graph is strongly connected and carries a Perron-Frobenius eigenvector for eigenvalue 3, whose entries record Lie-theoretic invariants (dimension, Gelfand-Kirillov dimension, or Bernstein number) of the corresponding modules.
2501.00291
This paper classifies the combinatorics of transitive module categories over the monoidal category of finite-dimensional sl3-modules, obtained by letting that category act on an arbitrary simple sl3-…