Irreducible representation of GL(D)

  • Thread starter gentsagree
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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
 

Answers and Replies

  • #2
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Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
 

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