Schubert classes in the equivariant cohomology of the Lagrangian Grassmannian
| dc.creator | Ikeda, Takeshi | |
| dc.date | 2005-08-05 | |
| dc.date | 2006-05-11 | |
| dc.date.accessioned | 2026-07-07T06:42:45Z | |
| dc.date.available | 2026-07-07T06:42:45Z | |
| dc.description | 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 $λ_1\leq n$ 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 $H_T^*(LG_n).$ | |
| dc.identifier | https://arxiv.org/abs/math/0508110 | |
| dc.identifier | http://arxiv.org/abs/math/0508110 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/102155 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Combinatorics | |
| dc.title | Schubert classes in the equivariant cohomology of the Lagrangian Grassmannian | |
| dc.type | text |