### Abstract

The coefficients of the Kazhdan-Lusztig polynomials P_{v};_{w}.q/ are nonnegative integers that are upper semicontinuous relative to Bruhat order. Conjecturally, the same properties hold for h-polynomials H_{v};_{w}.q/ of local rings of Schubert varieties. This suggests a parallel between the two families of polynomials. We prove our conjectures for Grassmannians, and more generally, covexillary Schubert varieties in complete flag varieties, by deriving a combinatorial formula for H_{v};_{w}.q/. We introduce drift configurations to formulate a new and compatible combinatorial rule for Pv;w.q/. From our rules we deduce, for these cases, the coefficient-wise inequality P_{v};_{w}.q/≤H_{v};_{w}.q/.

Original language | English (US) |
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Pages (from-to) | 594-623 |

Number of pages | 30 |

Journal | Algebra and Number Theory |

Volume | 5 |

Issue number | 5 |

DOIs | |

State | Published - 2011 |

### Keywords

- Hilbert series
- Kazhdan-lusztig polynomials
- Schubert varieties

### ASJC Scopus subject areas

- Algebra and Number Theory

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## Cite this

*Algebra and Number Theory*,

*5*(5), 594-623. https://doi.org/10.2140/ant.2011.5.595