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A promotion operator on rigged configurations

Abstract : In a recent paper, Schilling proposed an operator $\overline{\mathrm{pr}}$ on unrestricted rigged configurations $RC$, and conjectured it to be the promotion operator of the type $A$ crystal formed by $RC$. In this paper we announce a proof for this conjecture.
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Qiang Wang. A promotion operator on rigged configurations. 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009), 2009, Hagenberg, Austria. pp.881-892, ⟨10.46298/dmtcs.2702⟩. ⟨hal-01185394⟩

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