Promotion on Generalized Oscillating Tableaux and Web Rotation

TL;DR

This paper introduces a generalized promotion operation on oscillating tableaux and demonstrates its correspondence with web rotation in the context of irreducible A2-webs, extending classical combinatorial concepts.

Contribution

The paper defines a new generalized promotion operation on oscillating tableaux and links it to web rotation, broadening the understanding of tableau symmetries and web transformations.

Findings

Promotion on generalized oscillating tableaux corresponds to web rotation.

Establishes a connection between combinatorial tableaux and web symmetries.

Extends classical promotion to a broader combinatorial setting.

Abstract

We introduce the notion of a generalized oscillating tableau and define a promotion operation on such tableaux that generalizes the classical promotion operation on standard Young tableaux. As our main application, we show that this promotion corresponds to rotation of the irreducible $A_2$-webs of G. Kuperberg.