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 lambda = (lambda(1),..., lambda(k)) with lambda(1) <= n there is a Schubert variety X(lambda). Let T denote a maximal torus of the syrnplectic group acting on LG(n). Consider the T-equivariant cohoniology of LG(n) and the T-equivariant fundamental class or (lambda) of X(lambda). The main reSUlt of the present paper is an explicit formula for the restriction of the class sigma (lambda) 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 Giarnbelli-type formula for LG(n). As another consequence ofthe main result, we obtained a presentation of the ring H-T* (LG(n)). (c) 2007 Elsevier Inc. All rights reserved.