Restricted Kac modules of special Hamiltonian Lie superalgebras of odd type

Abstract

This paper aims to describe irreducible restricted modules of the special Hamiltonian Lie superalgebras of odd type over an algebraically closed field of characteristic [Formula: see text]. A sufficient and necessary condition for the restricted Kac modules to be irreducible is given in terms of typical weights. Furthermore, the character formulas for the irreducible quotients of the restricted Kac 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 [Formula: see text]-dimensional central extension of the classical Lie superalgebra of type [Formula: see text]. In particular, the composition factors of restricted Kac modules are determined in a sense.