现阶段典型模李超代数以及部分Cartan型模李超代数的表示已有较丰富的研究结果， 但是尚有部分Cartan型模李超代数的表示没有被研究，如特殊奇Hamilton超代数。因为特殊奇Hamilton超代数的表示目前尚无任何结果，所以本项目拟研究限制特殊奇Hamilton超代数的Kac模。项目的预期结果对模李超代数表示理论的发展具有一定的促进作用。项目的具体工作如下：.①利用广义根反射给出限制特殊奇Hamilton超代数的限制Kac模不可约的充分必要条件。.②利用限制特殊奇Hamilton超代数的限制Kac模的长度确定它的复型。进一步地，利用复型计算限制特殊奇Hamilton超代数的限制Kac模不可约商模的特征标公式。.③研究限制特殊奇Hamilton超代数的非限制Kac模的不可约性。

At the present stage, many deep results have been obtained for the representation of classical modular Lie superalgebras and a part of modular Lie superalgebras of Cartan type, but representation theory of some modular Lie superalgebras of Cartan type is still in the early stage, e.g. special Hamiltonian superalgebras of odd type. Since the representation theory of special Hamiltonian superalgebras of odd type is still in the early stage, in this project we will study Kac modules of restricted special Hamiltonian superalgebras of odd type. The expected results will promote the development of the representation theory of modular Lie superalgebras. The contents of the project are listed as follow:.①Use the generalized root reflections to give a sufficient and necessary condition for restricted Kac modules of restricted special Hamiltonian superalgebras of odd type to be irreducible..②Determine complex of the restricted Kac modules of restricted special Hamiltonian superalgebras of odd type by its length. Further, using this complex we can obtain character formulas for irreducible quotients of restricted Kac modules of restricted special Hamiltonian superalgebras of odd type..③Study the irreducibility of non-restricted Kac modules of restricted special Hamiltonian superalgebras of odd type.