### Abstract

For each infinite series of the classical Lie groups of type B, C or D, we introduce a family of polynomials parametrized by the elements of the corresponding Weyl group of infinite rank. These polynomials represent the Schubert classes in the equivariant cohomology of the corresponding flag variety. They satisfy a stability property, and are a natural extension of the (single) Schubert polynomials of Billey and Haiman, which represent non-equivariant Schubert classes. When indexed by maximal Grassmannian elements of the Weyl group, these polynomials are equal to the factorial analogues of Schur Q- or P-functions defined earlier by Ivanov.

Original language | English |
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Pages | 665-676 |

Number of pages | 12 |

Publication status | Published - 2008 |

Externally published | Yes |

Event | 20th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'08 - Valparaiso, Chile Duration: 2008 Jun 23 → 2008 Jun 27 |

### Other

Other | 20th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'08 |
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Country | Chile |

City | Valparaiso |

Period | 08/6/23 → 08/6/27 |

### Keywords

- Factorial Q-function
- Flag variety
- Schubert polynomial

### ASJC Scopus subject areas

- Algebra and Number Theory

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## Cite this

Ikeda, T., Mihalcea, L., & Naruse, H. (2008).

*Double Schubert polynomials for the classical Lie groups*. 665-676. Paper presented at 20th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'08, Valparaiso, Chile.