I'm taking a course on Lie groups and am reading alongisde Cahn's semi-simple lie algebras and their representations.(adsbygoogle = window.adsbygoogle || []).push({});

On page 4 he starts to construct a representation T of the Lie group corresponding to SU(2) acting on a linear space V, by defining the action of [itex]T_z[/itex] and [itex]T_+[/itex] on a vector [itex]v_j[/itex] by

[itex]T_z v_j = jv_j, \quad T_+ v_j = 0[/itex]

and then constructs a [itex](2j+1)[/itex]-dimensional representation.

I don't understand what allows him to assume that there exist vectors in V with this property.

Any help would be appreciated.

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# Representations of SU(2)

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