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- W2950331570 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 $lambda=(lambda_1,...,lambda_k)$ with $lambda_1leq n$ there is a Schubert variety $X(lambda).$ 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 $sigma(lambda)$ 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 Giambelli-type formula for $LG_n.$ As another consequence of the main result, we obtained a presentation of the ring $H_T^*(LG_n).$" @default.
- W2950331570 created "2019-06-27" @default.
- W2950331570 creator A5083895442 @default.
- W2950331570 date "2005-08-05" @default.
- W2950331570 modified "2023-09-27" @default.
- W2950331570 title "Schubert classes in the equivariant cohomology of the Lagrangian Grassmannian" @default.
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