Character Formulas for Simple Modules of Hamiltonian Lie Superalgebras of Odd Type

Abstract

In this paper, character formulas are explicitly characterized for all simple restricted modules of Hamiltonian Lie superalgebras of odd type over an algebraically closed field of characteristic $p \gt 3$. In the process we use the lengths and highest weights of simple quotients of restricted Kac modules of atypical weights with respect to a series of Borel subalgebras to determine the composition factors, composition series and the character formulas for the restricted Kac modules of atypical weights for the Lie superalgebras under consideration.