On linked modules over the super-Yangian of the superalgebra Q(1)

Abstract

Let Q(n) be the queer Lie superalgebra. We determine conditions under which two one-dimensional modules over the super-Yangian of Q(1) can be extended nontrivially, and thus belong to the same block of the subcategory of finite-dimensional YQ(1)-modules admitting generalized central character χ = 0. We use these results to determine conditions under which two one-dimensional modules over the finite W-algebra for Q(n) can be extended nontrivially. We describe blocks in the category of finite-dimensional modules over the finite W-algebra for Q(2). In certain cases, we determine conditions under which two simple finite-dimensional YQ(1)-modules admitting central character χ ≠ 0 can be extended nontrivially and propose a conjecture in the general case.