Tensor Product Decompositions, Limits in Excellent Filtrations, Affine Weyl Group Orbits, and Tableaux Counting
Representation Theory
2025-10-07 v1 Combinatorics
Abstract
We express the outer multiplicities in the tensor products of two fundamental simple modules for an affine Kac-Moody algebra of type in terms of counting certain sets of multipartitions by exploring the stabilizing limits of certain excellent filtrations. This extends for all ranks a previously obtained result by Jakeli\'c and the second author for rank . The same outer multiplicities were previously computed by Misra and Wilson in terms of counting certain sets of tableaux. By comparing these two expressions and by explicitly exhibiting a combinatorial description of level- affine Weyl group orbits, we establish the existence of a bijection between the Misra-Wilson set of tableaux and a disjoint union of certain sets of multipartitions.
Cite
@article{arxiv.2510.04697,
title = {Tensor Product Decompositions, Limits in Excellent Filtrations, Affine Weyl Group Orbits, and Tableaux Counting},
author = {Laura Estivalez and Adriano Moura},
journal= {arXiv preprint arXiv:2510.04697},
year = {2025}
}