On a generic Verma module at the critical level over affine Lie superalgebras

We describe the structure of a Verma module with a generic highest weight at the critical level over a symmetrizable affine Lie superalgebra not of the type A(2k,2l)^{(4)}. We obtain the character formula for a simple module with a generic highest weight at the critical level conjectured by V. G. Kac and D. A. Kazhdan.Comment: considerably revised text, including the title; 33 page

Bounded highest weight modules of q(n)

A classification of the simple highest weight bounded modules of the queer Lie superalgebras q(n) is obtained. To achieve this classification we introduce a new combinatorial tool - the star action. Our result leads in particular to a classification of all simple weight q(n)-modules.Comment: 40 pages, some corrections made to the earlier version. To appear in IMR