Diagrammatic description for the categories of perverse sheaves on isotropic Grassmannians

详细信息    查看全文

• 作者：Michael Ehrig ; Catharina Stroppel
• 刊名：Selecta Mathematica, New Series
• 出版年：2016
• 出版时间：July 2016
• 年：2016
• 卷：22
• 期：3
• 页码：1455-1536
• 全文大小：3,214 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  
• 出版者：Birkh盲user Basel
• ISSN：1420-9020
• 卷排序：22

文摘

For each integer \(k\ge 4\), we describe diagrammatically a positively graded Koszul algebra \(\mathbb {D}_k\) such that the category of finite dimensional \(\mathbb {D}_k\)-modules is equivalent to the category of perverse sheaves on the isotropic Grassmannian of type \(\mathrm{D}_k\) or \(\mathrm{B}_{k-1}\), 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.Mathematics Subject Classification05E1014M1517B1017B4555N9120C08