Irreducible representation of GL(D)

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Hi,

I'm reading: "Let [itex]v_{a}[/itex] represent a generic element of [itex]R^{D}[/itex]. The action of a non-singular linear operator on this space gives a D-dimensional irreducible representation V of GL(D); indeed, this representation defines the group itself".

I have a couple of questions:

1. How do I know that the rep will be IRREDUCIBLE? Is it a straightforward consequence of the linearity of the operators, or otherwise?

2. What does the last bit mean? Is it that the representation furnished by the action of linear ops on R is the "fundamental" of GL(D)?

Thanks
 

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