The weighted hook length formula III: Shifted tableaux

Abstract

Recently, a simple proof of the hook length formula was given via the branching rule. In this paper, we extend the results to shifted tableaux. We give a bijective proof of the branching rule for the hook lengths for shifted tableaux; present variants of this rule, including weighted versions; and make the first tentative steps toward a bijective proof of the hook length formula for d-complete posets.