Geodesic
2-row Springer Fibres and KhovanovDiagram Algebras for Type D
Canadian journal of mathematics, Tome 68 (2016) no. 6, pp. 1285-1333

Voir la notice de l'article provenant de la source Cambridge

DOI

We study in detail two row Springer fibres of even orthogonal type from an algebraic as well as a topological point of view. We show that the irreducible components and their pairwise intersections are iterated ${{\mathbb{P}}^{1}}$ -bundles. Using results of Kumar and Procesi we compute the cohomology ring with its action of the Weyl group. The main tool is a type $\text{D}$ diagram calculus labelling the irreducible components in a convenient way that relates to a diagrammatical algebra describing the category of perverse sheaves on isotropic Grassmannians based on work of Braden. The diagram calculus generalizes Khovanov's arc algebra to the type $\text{D}$ setting and should be seen as setting the framework for generalizing well-known connections of these algebras in type $\text{A}$ to other types.
DOI : 10.4153/CJM-2015-051-4
Mots-clés : 17-11, Springer fibers, Khovanov homology, Weyl group type D 
Ehrig, Michael; Stroppel, Catharina. 2-row Springer Fibres and KhovanovDiagram Algebras for Type D. Canadian journal of mathematics, Tome 68 (2016) no. 6, pp. 1285-1333. doi: 10.4153/CJM-2015-051-4
@article{10_4153_CJM_2015_051_4,
     author = {Ehrig, Michael and Stroppel, Catharina},
     title = {2-row {Springer} {Fibres} and {KhovanovDiagram} {Algebras} for {Type} {D}},
     journal = {Canadian journal of mathematics},
     pages = {1285--1333},
     year = {2016},
     volume = {68},
     number = {6},
     doi = {10.4153/CJM-2015-051-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2015-051-4/}
}
TY  - JOUR
AU  - Ehrig, Michael
AU  - Stroppel, Catharina
TI  - 2-row Springer Fibres and KhovanovDiagram Algebras for Type D
JO  - Canadian journal of mathematics
PY  - 2016
SP  - 1285
EP  - 1333
VL  - 68
IS  - 6
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-2015-051-4/
DO  - 10.4153/CJM-2015-051-4
ID  - 10_4153_CJM_2015_051_4
ER  - 
%0 Journal Article
%A Ehrig, Michael
%A Stroppel, Catharina
%T 2-row Springer Fibres and KhovanovDiagram Algebras for Type D
%J Canadian journal of mathematics
%D 2016
%P 1285-1333
%V 68
%N 6
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-2015-051-4/
%R 10.4153/CJM-2015-051-4
%F 10_4153_CJM_2015_051_4

Cité par Sources :