Torus fixed points in Schubert varieties and normalized median Genocchi numbers

Abstract

We give a new proof for the fact that the number of torus fixed points for the degenerated flag variety is equal to the normalized median Genocchi number, using the identification with a certain Schubert variety. We further study the torus fixed points for the symplectic degenerated flag variety and develop a combinatorial model, symplectic Dellac configurations, so parametrize them. The number of these symplectic fixed points is conjectured to be the median Euler number.

title changed, 12 pages, to appear in Séminaire Lotharingien de Combinatoire