Degenerate flag varieties and the median genocchi numbers

Evgeny Feigin*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We study the GMa degenerations Fa λ of the type A flag varieties Fλ. We describe these degenerations explicitly as subvarieties in the products of Grassmannians. We construct cell decompositions of Fa λ and show that for complete flags the number of cells is equal to the normalized median Genocchi numbers hn. This leads to a new combinatorial definition of the numbers hn. 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 languageEnglish
Pages (from-to)1163-1178
Number of pages16
JournalMathematical Research Letters
Issue number6
StatePublished - Nov 2011
Externally publishedYes


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