Rubey's evacuation–reversal conjecture for vacillating tableaux

Let TT be a standard Young tableau with at most three rows, whose rows are all of even length or all of odd length. Let ε(T)\varepsilon(T) denote the evacuation of TT. A vacillating tableau of shape \emptyset is associated to each such tableau.

Rubey's conjecture. The vacillating tableau corresponding to ε(T)\varepsilon(T) is the reversal of the vacillating tableau corresponding to TT.

This conjecture predicts that evacuation of the standard Young tableau is reflected by reversal of the associated vacillating tableau. The source gives no resolution, so its status remains open.

Sources & referencesView supporting material

Primary source

Judith Braunsteiner, “A Sundaram type bijection for SO(3): vacillating tableaux and pairs of standard Young tableaux and orthogonal Littlewood-Richardson tableaux”, arXiv:1801.03780 (2018).

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