Gabriel Frieden - Affine type A geometric crystal structure on the Grassmannian

dmtcs:6393 - Discrete Mathematics & Theoretical Computer Science, April 22, 2020, DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016) - https://doi.org/10.46298/dmtcs.6393
Affine type A geometric crystal structure on the GrassmannianArticle

Authors: Gabriel Frieden 1

  • 1 Department of Mathematics [Ann Arbor]

We construct a type A(1) n−1 affine geometric crystal structure on the Grassmannian Gr(k, n). The tropicalization of this structure recovers the combinatorics of crystal operators on semistandard Young tableaux of rectangular shape (with n − k rows), including the affine crystal operator e 0. In particular, the promotion operation on these tableaux essentially corresponds to cyclically shifting the Plu ̈cker coordinates of the Grassmannian.


Volume: DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016)
Published on: April 22, 2020
Imported on: July 4, 2016
Keywords: [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]
Funding:
    Source : OpenAIRE Graph
  • Incentive - LA 22 - 2013; Funder: Fundação para a Ciência e a Tecnologia, I.P.; Code: Incentivo/EME/LA0022/2013

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