Diagrammatic description for the categories of perverse sheaves on isotropic Grassmannians

Michael Ehrig ^[1] ; Catharina Stroppel ^[1]
1. [1] Universität Bonn
Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 22, Nº. 3, 2016, págs. 1455-1536
Idioma: inglés
DOI: 10.1007/s00029-015-0215-9
Enlaces
- Texto completo
Resumen
- For each integer k≥4k≥4 , we describe diagrammatically a positively graded Koszul algebra DkDk such that the category of finite dimensional DkDk -modules is equivalent to the category of perverse sheaves on the isotropic Grassmannian of type DkDk or Bk−1Bk−1 , constructible with respect to the Schubert stratification. The algebra is obtained by a (non-trivial) “folding” procedure from a generalized Khovanov arc algebra. Properties such as graded cellularity and explicit closed formulas for graded decomposition numbers are established by elementary tools.