### 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 λ = (λ_{1}, ..., λ_{k}) with λ_{1} ≤ 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}).

Original language | English |
---|---|

Pages (from-to) | 1-23 |

Number of pages | 23 |

Journal | Advances in Mathematics |

Volume | 215 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2007 Oct 20 |

Externally published | Yes |

### Keywords

- Equivariant cohomology
- Factorial Q-functions
- Lagrangian Grassmannian
- Schubert classes

### ASJC Scopus subject areas

- Mathematics(all)