Séminaire Lotharingien de Combinatoire, 82B.95 (2019), 12 pp.

Dave Anderson, Takeshi Ikeda, Minyoung Jeon, and Ryotaro Kawago

Multiplicities of Schubert varieties in the symplectic flag variety

Abstract. Let Ωw be a Schubert variety in the symplectic flag variety, and let ev in Ωw be a torus fixed point. We give a combinatorial formula for the Hilbert-Samuel multiplicity of Ωw at the point ev, in the case where 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.

Received: November 15, 2018. Accepted: February 17, 2019. Final version: April 1, 2019.

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