Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.14879 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- We study the structure of tensor products of $\mathfrak{gl}(\infty) = \varinjlim \mathfrak{gl}(n)$-modules $\mathbf L(\mathbf λ) \otimes \mathbf F$ where $\mathbf L(\mathbf λ)$ is a simple integrable highest weight module and $\mathbf F$ is a simple integrable weight multiplicity-free module. Both $\mathbf L(\mathbf λ)$ and $\mathbf F$ are infinite dimensional, in particular $\mathbf F$ can be a Fock module. Similar tensor products of $\mathfrak{gl}(n)$-modules are semisimple and their simple constituents are described by the classical Pieri rule. We prove that a $\mathfrak{gl}(\infty)$-module $\mathbf M:= \mathbf L(\mathbf λ) \otimes \mathbf F$ is semisimple only in relatively trivial cases, and is indecomposable otherwise. Our main results are a description of the simple constituents of $\mathbf M$, and the construction of a linkage filtration on $\mathbf M$ that provides information on when two simple constituents of $\mathbf M$ are linked. Using the linkage filtration, we compute the socle and radical filtrations of $\mathbf M$, and determine when $\mathbf M$ is rigid.