Schubert classes in the equivariant cohomology of the Lagrangian Grassmannian
By Takeshi Ikeda. 2005
49 citations recorded by the source corpus.
Abstract Let LG n denote the Lagrangian Grassmannian parametrizing maximal isotropic (Lagrangian) subspaces of a fixed symplectic vector space of dimension 2n. For each strict partition λ = ( λ 1 , … , λ k ) with λ 1 ⩽ n there is a Schubert variety X ( λ ) . Let T denote a maximal torus of the symplectic group acting on LG n . Consider the T-equivariant cohomology of LG n and the T-equivariant fundamental class σ ( λ ) of X ( λ ) . The main result of the present paper is an explicit formula for the restriction of the class σ ( λ ) to any torus fixed point. The formula is written in terms of factorial analogue of the Schur Q-function, introduced by Ivanov. As a corollary to the restriction formula, we obtain an equivariant version of the Giambelli-type formula for LG n . As another consequence of the main result, we obtained a presentation of the ring H T ∗ ( LG n ) .
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/5a6b24d7805d055bf052f483d438d732febe940f
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Citations in the corpus
- K-theoretic analogues of factorial Schur P- and Q-functions (2011, methodology): “In [8], we simply called Ivanov’s function the factorial Schur Q-function.”
- Double Schubert polynomials for the classical groups (2008, methodology): “For the Lagrangian Grassmannian, the first author [16] identified the equivariant Schubert classes with the factorial analogues of Schur Q-function defined by Ivanov [20].”