Multiplicities of Schubert varieties in the symplectic flag variety

Dave Anderson, Takeshi Ikeda, Minyoung Jeon, Ryotaro Kawago

Research output: Contribution to conferencePaper

Abstract

Let Ww be a Schubert variety in the symplectic flag variety, and let ev 2 Ww be a torus fixed point. We give a combinatorial formula for the Hilbert-Samuel multiplicity of Ww at the point ev, in the case where w is a vexillary signed permutation. Our formula is phrased in terms of excited Young diagrams, extending results by Ghorpade-Raghavan and Ikeda-Naruse for Grassmannians, as well as Li-Yong for vexillary Schubert varieties in type A flag manifolds.

Original languageEnglish
Publication statusPublished - 2019
Event31st International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2019 - Ljubljana, Slovenia
Duration: 2019 Jul 12019 Jul 5

Conference

Conference31st International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2019
CountrySlovenia
CityLjubljana
Period19/7/119/7/5

Keywords

  • Multiplicity
  • Schubert variety
  • Vexillary permutation

ASJC Scopus subject areas

  • Algebra and Number Theory

Fingerprint Dive into the research topics of 'Multiplicities of Schubert varieties in the symplectic flag variety'. Together they form a unique fingerprint.

  • Cite this

    Anderson, D., Ikeda, T., Jeon, M., & Kawago, R. (2019). Multiplicities of Schubert varieties in the symplectic flag variety. Paper presented at 31st International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2019, Ljubljana, Slovenia.