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comment A request for suggestions of advanced topics in representation theory
Thank you very much! I will take a look at this reference.
Jul
7
comment A request for suggestions of advanced topics in representation theory
@Emerton Dear Matthew, Thank you very much for these suggestions; I really appreciate it. Could you please suggest a reference for the geometric perspective? If it is not too general a question to ask (but it probably is), then I would also be interested in the possible steps that one could take to get toward research in the representation theory of Lie groups and Lie algebras and related areas (say, after Knapp's book); more precisely, are there other important/essential topics that one should learn before/while reading research papers? Thank you very much and best regards,
Jul
6
comment A request for suggestions of advanced topics in representation theory
@JimHumphreys Thank you very much for pointing this out; I have converted the question to community-wiki.
Jul
6
revised A request for suggestions of advanced topics in representation theory
convert to community-wiki
Jul
6
comment A request for suggestions of advanced topics in representation theory
@JustinCampbell I think that the coverage of Bump's book is broader than simply the representation theory of $\mathfrak{sl}_{2}$. Of course, chapter 12 is entitled "Representations of $\mathfrak{sl}_{2}(\mathbb{C})$" but there are 50 chapters in Bump's book and many of them discuss a wide range of different topics. For example, general semisimple compact Lie groups are studied in chapter 23. Also, standard topics such as root systems, heighest-weight theory, the Iwasawa and Bruhat decompositions, symmetric spaces etc. are discussed in chapters 1 - 33 (i.e., the first two parts of the book).
Jul
6
asked A request for suggestions of advanced topics in representation theory