Maria Monks Gillespie ; Jake Levinson - Monodromy and K-theory of Schubert curves via generalized jeu de taquin

dmtcs:6381 - 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.6381
Monodromy and K-theory of Schubert curves via generalized jeu de taquinArticle

Authors: Maria Monks Gillespie 1; Jake Levinson 2

We establish a combinatorial connection between the real geometry and the K-theory of complex Schubert curves Spλ‚q, which are one-dimensional Schubert problems defined with respect to flags osculating the rational normal curve. In a previous paper, the second author showed that the real geometry of these curves is described by the orbits of a map ω on skew tableaux, defined as the commutator of jeu de taquin rectification and promotion. In particular, the real locus of the Schubert curve is naturally a covering space of RP1, with ω as the monodromy operator.We provide a fast, local algorithm for computing ω without rectifying the skew tableau, and show that certain steps in our algorithm are in bijective correspondence with Pechenik and Yong's genomic tableaux, which enumerate the K-theoretic Littlewood-Richardson coefficient associated to the Schubert curve. Using this bijection, we give purely combinatorial proofs of several numerical results involving the K-theory and real geometry of Spλ‚q.


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
  • Algebraic Combinatorics; Funder: National Science Foundation; Code: 1101152
  • Combinatorics in Geometry, Physics, and Representation Theory; Funder: National Science Foundation; Code: 1464693
  • Arithmetic of automorphic forms: cycles, periods and p-adic L-functions; Funder: National Science Foundation; Code: 1160720

4 Documents citing this article

Consultation statistics

This page has been seen 186 times.
This article's PDF has been downloaded 165 times.