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One of the most important groups in physics is the group of complex unimodular matrices

[tex] \mbox{SL}\left(2,\mathbb{C}\right)=:\left\{A\in \mathcal{M}_{2}\left(\mathbb{C}\right)|\mbox{det} A=1\right\} [/tex]

This is a Lie group.I haven't seen any decent physics book in which the theory of this group is presented.

So I'm asking you to give me a reference on a book which would contain

1.The irreducible representations of this group.

2.The operators which generate the Lie algebra of this group and the commutation relations which define the Lie algebra.

3.How is the space of this (the group's) representations constructed and what is the action of operators on its basis.

4.Irreducible representations of the Lie algebra of this group.(Operators,base & action of operators on the base).

5.The connection (if any) between irreducible representations of the group & of its algebra.

6.The connections (if any) between the irreducible representations of this group & algebra and the group [itex] \mbox{SU(2)} [/itex] and its Lie algebra [itex] \mbox{su(2)} [/itex]...How are all operators connected (if so) ?

Daniel.

[tex] \mbox{SL}\left(2,\mathbb{C}\right)=:\left\{A\in \mathcal{M}_{2}\left(\mathbb{C}\right)|\mbox{det} A=1\right\} [/tex]

This is a Lie group.I haven't seen any decent physics book in which the theory of this group is presented.

So I'm asking you to give me a reference on a book which would contain

1.The irreducible representations of this group.

2.The operators which generate the Lie algebra of this group and the commutation relations which define the Lie algebra.

3.How is the space of this (the group's) representations constructed and what is the action of operators on its basis.

4.Irreducible representations of the Lie algebra of this group.(Operators,base & action of operators on the base).

5.The connection (if any) between irreducible representations of the group & of its algebra.

6.The connections (if any) between the irreducible representations of this group & algebra and the group [itex] \mbox{SU(2)} [/itex] and its Lie algebra [itex] \mbox{su(2)} [/itex]...How are all operators connected (if so) ?

Daniel.

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