Extension Quiver for Lie Superalgebra $\mathfrak{q}(3)$

Symmetry Integrability and Geometry-Methods and Applications

article

Nikolay Grantcharov¹  Vera Serganova² 

[1] Department of Mathematics, University of Chicago;Department of Mathematics, University of California at Berkeley

关键词: Lie superalgebra;    extension quiver;    cohomology;    flag supermanifold 2020 Mathematics Subject Classification 17B55;    17B10;   

DOI  :  10.3842/SIGMA.2020.141

来源: National Academy of Science of Ukraine

【 摘 要 】

We describe all blocks of the category of finite-dimensional $\mathfrak{q}(3)$-supermodules by providing their extension quivers. We also obtain two general results about the representation of $\mathfrak{q}(n)$: we show that the Ext quiver of the standard block of $\mathfrak{q}(n)$ is obtained from the principal block of $\mathfrak{q}(n-1)$ by identifying certain vertices of the quiver and prove a ''virtual'' BGG-reciprocity for $\mathfrak{q}(n)$. The latter result is used to compute the radical filtrations of $\mathfrak{q}(3)$ projective covers.

【 授权许可】

Unknown