The Irreducible Unitary Representation of SU(2) and Its Lie algebra Representations

Abstract

We study the three dimensional special unitary group  whose the Lie algebra is given by   . The research aims to construct a representation of  and  realized on the inner product  space  of all homogeneous polinomials of degree  and  of all homogeneous polinomials of degree  which satisfying  irreducibility and unitarity conditions. Namely, The action of    and  are presented on the spaces  and  respectively. In the first step, we computed all representations of  on  and .   Furthermore, in the second step, by simply connectedness property of  then the irreducible unitary representation of Lie algebra  realized on  can be obtained from the  representation by using derived representation. The results showed the explicit formulas of representations of    and