Abstract
In their study of the equivariant K-theory of the generalized flag varieties G/P, where G is a complex semisimple Lie group, and P is a parabolic subgroup of G, Lenart and Postnikov introduced a combinatorial tool, called the alcove path model. It provides a model for the highest weight crystals with dominant integral highest weights, generalizing the model by semistandard Young tableaux. In this paper, we prove a simple and explicit formula describing the crystal isomorphism between the alcove path model and the Gelfand–Tsetlin pattern model for type A.
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Acknowledgements
HW would like to thank Susumu Ariki for bringing his attention to this topic. The authors are grateful to the referees for careful readings and helpful comments.
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Communicated by Jang Soo Kim.
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Watanabe, H., Yamamura, K. Alcove Paths and Gelfand–Tsetlin Patterns. Ann. Comb. 25, 645–676 (2021). https://doi.org/10.1007/s00026-021-00544-5
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DOI: https://doi.org/10.1007/s00026-021-00544-5