# Toric degenerations of flag varieties from matching field tableaux

## TL;DR

This paper introduces a new family of tableaux bridging classical and matching field tableaux, leading to toric degenerations of flag varieties via SAGBI bases and initial ideals.

## Contribution

It constructs interpolating tableaux families that produce toric degenerations of flag varieties through SAGBI bases of Plücker algebras.

## Key findings

- Families of tableaux interpolate between classical and matching field tableaux.
- Each family yields a toric ideal as an initial of the Plücker ideal.
- Results in new toric degenerations of flag varieties.

## Abstract

We present families of tableaux which interpolate between the classical semi-standard Young tableaux and matching field tableaux. Algebraically, this corresponds to SAGBI bases of Pl\"ucker algebras. We show that each such family of tableaux leads to a toric ideal, that can be realized as initial of the Pl\"ucker ideal, hence a toric degeneration for the flag variety.