Extension Quiver for Lie Superalgebra 𝖖(3)

Abstract

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