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This is a Quantitative Study study.

October 10, 2025Open Access

Tensor Product Decompositions, Limits in Excellent Filtrations, Affine Weyl Group Orbits, and Tableaux Counting

Key Points

A bijection exists between Misra-Wilson tableaux and multipartitions, illuminating their combinatorial structure.
The study extends earlier results for rank 1 to all ranks, confirming outer multiplicities in Kac-Moody algebras.
Connections between tensor product decompositions and excellent filtrations provide new insights into algebraic structures.
Counted multipartitions and tableaux counting reveal important relationships in the theory of affine Weyl groups.

Abstract

We express the outer multiplicities in the tensor products of two fundamental simple modules for an affine Kac-Moody algebra of type A 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 Jakelić and the second author for rank 1. 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-2 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.

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Cite This Study

Estivalez et al. (Mon,) studied this question.

synapsesocial.com/papers/68e997abe14057276da7f1eb https://doi.org/https://doi.org/10.48550/arxiv.2510.04697

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