Schubert classes in the equivariant cohomology of the Lagrangian Grassmannian

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Let LGₙ denote the Lagrangian Grassmannian parametrizing maximal isotropic (Lagrangian) subspaces of a fixed symplectic vector space of dimension 2n. For each strict partition λ=(λ₁,...,λₖ) with λ₁≤ n there is a Schubert variety X(λ). Let T denote a maximal torus of the symplectic group acting on LGₙ. Consider the T-equivariant cohomology of LGₙ 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 LGₙ. As another consequence of the main result, we obtained a presentation of the ring Hₜ*(LGₙ).