## Abstract

We study the G^{M}_{a} degenerations F^{a} _{λ} of the type A flag varieties F_{λ}. We describe these degenerations explicitly as subvarieties in the products of Grassmannians. We construct cell decompositions of F^{a} _{λ} and show that for complete flags the number of cells is equal to the normalized median Genocchi numbers h_{n}. This leads to a new combinatorial definition of the numbers h_{n}. We also compute the Poincaré polynomials of the complete degenerate flag varieties via a natural statistics on the set of Dellac's configurations, similar to the length statistics on the set of permutations. We thus obtain a natural q-version of the normalized median Genocchi numbers.

Original language | English |
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Pages (from-to) | 1163-1178 |

Number of pages | 16 |

Journal | Mathematical Research Letters |

Volume | 18 |

Issue number | 6 |

DOIs | |

State | Published - Nov 2011 |

Externally published | Yes |