Monodromy and K-theory of Schubert curves via generalized jeu de taquin
Abstrak
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.
Topik & Kata Kunci
Penulis (2)
Maria Monks Gillespie
Jake Levinson
Akses Cepat
- Tahun Terbit
- 2020
- Sumber Database
- DOAJ
- DOI
- 10.46298/dmtcs.6381
- Akses
- Open Access ✓