No 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 prove a virtual BGG-reciprocity for q(n). The latter result is used to compute the radical filtrations of q(3) projective covers.

In this paper the authors introduce a class of parabolic subalgebras for classical simple Lie superalgebras associated to the detecting subalgebras introduced by Boe, Kujawa and Nakano. These parabolic subalgebras are shown to have good cohomological properties governed by the Bott-Borel-Weil theorem involving the zero component of the Lie superalgebra in conjunction with the odd roots. These results are later used to verify an open conjecture given by Boe, Kujawa and Nakano pertaining to the equality of various support varieties.