Dual Weight and Monodromy of Dual Affine RS Correspondence

Abstract

The dual affine Robinson--Schensted correspondence and the affine matrix-ball construction give two related parametrizations of extended affine permutations. From the stable-window data of the dual correspondence, we introduce a dual weight \(β\) and prove that it is consistent with the original pair \((λ,N_0)\). We prove that \(β\) and the AMBC weight \(ρ\) have identical monodromy along affine Knuth paths. We further give an explicit relation between \(β\) and \(ρ\), showing that their difference depends only on the associated tabloids.