Semigroups of $sl_3(\mathbb{C})$ tensor product invariants

TL;DR

This paper computes presentations for semigroup algebras related to $sl_3(C)$ tensor product decompositions and discovers new toric degenerations of the Grassmannian $Gr_3(C^n)$ that are invariant under the diagonal torus.

Contribution

It introduces new presentations for semigroup algebras associated with $sl_3(C)$ tensor products and identifies novel toric degenerations of the Grassmannian variety.

Findings

New semigroup algebra presentations for $sl_3(C)$ tensor products

Identification of new toric degenerations of $Gr_3(C^n)$

Enhanced understanding of $T$-invariant structures in algebraic geometry

Abstract

We compute presentations for a family of semigroup algebras related to the problem of decomposing $sl_3(\mathbb{C})$ tensor products. Along the way we find new toric degenerations of the Grassmannian variety $Gr_3(\mathbb{C}^n)$ which $T-$invariant for $T \subset GL_n(\mathbb{C})$ the diagonal torus.