Geodesic
Degenerate flag varieties: moment graphs and Schröder numbers
Journal of Algebraic Combinatorics, Tome 38 (2013) no. 1, pp. 159-189.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We study geometric and combinatorial properties of the degenerate flag varieties of type A. These varieties are acted upon by the automorphism group of a certain representation of a type A quiver, containing a maximal torus T. Using the group action, we describe the moment graphs, encoding the zero- and one-dimensional T-orbits. We also study the smooth and singular loci of the degenerate flag varieties. We show that the Euler characteristic of the smooth locus is equal to the large Schröder number and the Poincaré polynomial is given by a natural statistics counting the number of diagonal steps in a Schröder path. As an application we obtain a new combinatorial description of the large and small Schröder numbers and their q-analogues.
Keywords: Schröder numbers, moment graphs, flag varieties, quiver grassmannians 
@article{JAC_2013__38_1_a3,
     author = {Cerulli Irelli, Giovanni and Feigin, Evgeny and Reineke, Markus},
     title = {Degenerate flag varieties: moment graphs and {Schr\"oder} numbers},
     journal = {Journal of Algebraic Combinatorics},
     pages = {159--189},
     publisher = {mathdoc},
     volume = {38},
     number = {1},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2013__38_1_a3/}
}
TY  - JOUR
AU  - Cerulli Irelli, Giovanni
AU  - Feigin, Evgeny
AU  - Reineke, Markus
TI  - Degenerate flag varieties: moment graphs and Schröder numbers
JO  - Journal of Algebraic Combinatorics
PY  - 2013
SP  - 159
EP  - 189
VL  - 38
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JAC_2013__38_1_a3/
LA  - en
ID  - JAC_2013__38_1_a3
ER  - 
%0 Journal Article
%A Cerulli Irelli, Giovanni
%A Feigin, Evgeny
%A Reineke, Markus
%T Degenerate flag varieties: moment graphs and Schröder numbers
%J Journal of Algebraic Combinatorics
%D 2013
%P 159-189
%V 38
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JAC_2013__38_1_a3/
%G en
%F JAC_2013__38_1_a3
Cerulli Irelli, Giovanni; Feigin, Evgeny; Reineke, Markus. Degenerate flag varieties: moment graphs and Schröder numbers. Journal of Algebraic Combinatorics, Tome 38 (2013) no. 1, pp. 159-189. http://geodesic.mathdoc.fr/item/JAC_2013__38_1_a3/