Excited Young diagrams and equivariant Schubert calculus
By Takeshi Ikeda, H. Naruse. 2007
105 citations recorded by the source corpus.
We describe the torus-equivariant cohomology ring of isotropic Grassmannians by using a localization map to the torus fixed points. We present two types of formulas for equivariant Schubert classes of these homogeneous spaces. The first formula involves combinatorial objects which we call "excited Young diagrams", and the second one is written in terms of factorial Schur Q- or P-functions. As an application, we give a Giambelli-type formula for the equivariant Schubert classes. We also give combinatorial and Pfaffian formulas for the multiplicity of a singular point in a Schubert variety.
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/1812d3dc0a606dad9f0c45e05c0f9f7653e200ed
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In Discrete Mathematics and Combinatorics
- H. Naruse
- Megumi Harada
- Takeshi Ikeda
- Julianna Tymoczko
- Leonardo Constantin Mihalcea
- Martha Precup
- M. Masuda
- T. Horiguchi
In Geometry and Topology
- H. Naruse
- Megumi Harada
- Takeshi Ikeda
- Julianna Tymoczko
- Leonardo Constantin Mihalcea
- Martha Precup
- M. Masuda
- T. Horiguchi
In Mathematical Physics
Citations in the corpus
- Poset pinball, GKM-compatible subspaces, and Hessenberg varieties (2010, background): “the product structure of equivariant cohomology rings (see for instance [18,20,22,24,35]).”
- K-theoretic analogues of factorial Schur P- and Q-functions (2011, methodology): “See for example [1], [10] (note that our convention here is different from there).”
- Double Schubert polynomials for the classical groups (2008, background): “Note that Bw = 2−s(w)Cw, where s(w) is the number of signs changed by w (cf. Section 3.3 below).”