TY - JOUR
T1 - Degenerate flag varieties
T2 - Moment graphs and Schröder numbers
AU - Cerulli Irelli, Giovanni
AU - Feigin, Evgeny
AU - Reineke, Markus
N1 - Funding Information:
Acknowledgements The work of Evgeny Feigin was partially supported by the Russian President Grant MK-3312.2012.1, by the Dynasty Foundation, by the AG Laboratory HSE, RF government grant, ag. 11.G34.31.0023, by the RFBR grants 12-01-00070, 12-01-00944 and by the Russian Ministry of Education and Science under the grant 2012-1.1-12-000-1011-016. This study comprises research fundings from the ‘Representation Theory in Geometry and in Mathematical Physics’ carried out within The National Research University Higher School of Economics’ Academic Fund Program in 2012, grant No. 12-05-0014. This study was carried out within the National Research University Higher School of Economics Academic Fund Program in 2012–2013, research grant No. 11-01-0017. G.C.I. thanks Francesco Esposito for helpful discussions.
PY - 2013/8
Y1 - 2013/8
N2 - 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.
AB - 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.
KW - Flag varieties
KW - Moment graphs
KW - Quiver Grassmannians
KW - Schröder numbers
UR - https://www.scopus.com/pages/publications/84879691575
U2 - 10.1007/s10801-012-0397-6
DO - 10.1007/s10801-012-0397-6
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AN - SCOPUS:84879691575
SN - 0925-9899
VL - 38
SP - 159
EP - 189
JO - Journal of Algebraic Combinatorics
JF - Journal of Algebraic Combinatorics
IS - 1
ER -