Schubert classes in the equivariant cohomology of the Lagrangian Grassmannian

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 = (λ₁, ..., λ_k) with λ₁ ≤ 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).