Monodromy and K-theory of Schubert curves via generalized jeu de taquin
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...
Gespeichert in:
| Veröffentlicht in: | Discrete mathematics and theoretical computer science Jg. DMTCS Proceedings, 28th... |
|---|---|
| Hauptverfasser: | , |
| Format: | Journal Article Tagungsbericht |
| Sprache: | Englisch |
| Veröffentlicht: |
DMTCS
22.04.2020
Discrete Mathematics & Theoretical Computer Science |
| Schlagworte: | |
| ISSN: | 1365-8050, 1462-7264, 1365-8050 |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Zusammenfassung: | 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. |
|---|---|
| ISSN: | 1365-8050 1462-7264 1365-8050 |
| DOI: | 10.46298/dmtcs.6381 |