ABSTRACT: Some new representations of the supersymmetric transformations are derived, and the supermultiplets are introduced. Based on these representations, Graded Lie Algebras and various formulations (equations, commutation relations, propagators, Jacobi identities, etc.) of bosons and fermions may be unified. On the one hand, the mathematical characteristic of particles is proposed: bosons correspond to real number, and fermions correspond to imaginary number, respectively. Such fermions of even (or odd) number form bosons (or fermions), which is just consistent with a relation between imaginary and real number. The imaginary number is only included in the equations, forms, and matrixes of fermions. It is connected with relativity. On the other hand, the unified forms of supersymmetry are also connected with the statistics unifying Bose-Einstein and Fermi-Dirac statistics, and with the possible violation of Pauli exclusion principle; and a unified partition function is obtained. Moreover, three quarks may be described by the Borromean rings. Some unifications in particle physics are discussed. The quantum statistics is unified by the nonlinear equations. Based on the gauge groups, various unifications of interactions are researched. A developed direction of particle physics and modern science is possibly the higher dimensional complex space.