2019 | OriginalPaper | Chapter
Cluster Decorated Geometric Crystals, Generalized Geometric RSK-Correspondences, and Donaldson-Thomas Transformations
Author : Gleb Koshevoy
Published in: 2017 MATRIX Annals
Publisher: Springer International Publishing
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For a simply connected, connected, semisimple complex algebraic group G, we define two geometric crystals on the A $$\mathscr A$$ -cluster variety of double Bruhat cell B −∩ Bw 0 B. These crystals are related by the ∗ duality. We define the graded Donaldson-Thomas correspondence as the crystal bijection between these crystals. We show that this correspondence is equal to the composition of the cluster chamber Ansatz, the inverse generalized geometric RSK-correspondence, and transposed twist map due to Berenstein and Zelevinsky.