Restricted Kac modules of special Hamiltonian Lie superalgebras of odd type

This paper aims to describe irreducible restricted modules of the special Hamiltonian Lie superalgebras of odd type over an algebraically closed field of characteristic p > 3. A sufficient and necessary condition for the restricted Mac modules to be irreducible is given in terms of typical weights. Furthermore, the character formulas for the irreducible quotients of the restricted Mac modules are reduced to the ones for the irreducible quotients of the restricted Kac modules of the Hamiltonian Lie superalgebras of odd type and the ones of a 1-dimensional central extension of the classical Lie superalgebra of type (P) over tilde (n). In particular, the composition factors of restricted Mac modules are determined in a sense.