Balanced shifted tableaux

TL;DR

This paper introduces balanced shifted tableaux for root systems of type B and C, establishing a bijection with standard Young tableaux of shifted shape, thus extending combinatorial tableau theory.

Contribution

It defines balanced shifted tableaux for types B and C and proves their equinumerosity with standard Young tableaux via an explicit bijection.

Findings

Balanced shifted tableaux are introduced for types B and C.

A bijection between balanced shifted tableaux and standard Young tableaux is constructed.

Balanced shifted tableaux are shown to be equinumerous with standard Young tableaux.

Abstract

We introduce balanced shifted tableaux, as an analogue of balanced tableaux of Edelman and Greene, from the perspective of root systems of type B and C. We show that they are equinumerous to standard Young tableaux of the corresponding shifted shape by presenting an explicit bijection.