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I am trying to find books similar in the spirit of Ram Murty's Problems in Analytic Number theory or Murty Esmonde's Problems in Algebraic number theory in the field of Representation Theory (of groups, algebras, Lie algebras, possibly even goes in the direction of quivers). I want a book which doesn't provide details but directs me in the right direction via lots of exercises. One other book that kind of fits this category maybe Farb and Dennis's Noncommutative Algebra. But it is not purely focused on representation theory although some of the topics are. Any other suggestions?

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Kirillov’s Elements of the theory of representations is written in quite this spirit. From the original MR:

The book includes a large number of “exercises” (with hints for proving them), most of them being in fact very nontrivial sketches of results in and out of the literature, or playing an essential role in the proofs of the theorems.

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The books by Onishchik-Vinberg and by Etingof et al. might fit into this category, too.

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