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?
$\begingroup$
$\endgroup$
1
-
7$\begingroup$ So you like it tough, but do you like it Pavel Etingof, Oleg Golberg, Sebastian Hensel, Tiankai Liu, Alex Schwendner, Dmitry Vaintrob, and Elena Yudovina, Introduction to representation theory tough? Also, Sophie Morel's Representation theory notes come with a ton of exercises. $\endgroup$– darij grinbergCommented Apr 28, 2019 at 4:04
Add a comment
|
3 Answers
$\begingroup$
$\endgroup$
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.
$\begingroup$
$\endgroup$
4
The books by Onishchik-Vinberg and by Etingof et al. might fit into this category, too.
-
-
$\begingroup$ Is the Onischik and Vinberg book you have in mind Lie groups and algebraic groups (MSN), Lie groups and Lie algebras I (MSN), or another one? $\endgroup$– LSpiceCommented Apr 28, 2019 at 21:05
-
$\begingroup$ I imagine it is the first one (Lie groups and algebraic groups) $\endgroup$– dstrCommented Apr 29, 2019 at 16:31
-
$\begingroup$ @LSpice: Yes, I was too busy at the time to consult the book itself, which is on my shelf. $\endgroup$ Commented May 2, 2019 at 14:09
$\begingroup$
$\endgroup$
There is also the book by William Fulton and Joe Harris : Representation Theory (Springer, corrected edition,551 pages). It contains many exercises, with hints, answers, and references (pp. 516-535).