Finite-dimensional representations of periplectic Lie superalgebras

We study categories of finite-dimensional modules over the periplectic Lie superalgebras and obtain a BGG type reciprocity. In particular, we prove that these categories have only finitely-many blocks. We also compute the characters for irreducible modules over periplectic Lie superalgebras of ranks 2 and 3, and obtain explicit description of the blocks for ranks 2, 3, and 4. (C) 2015 Elsevier Inc. All rights reserved.