By now I have the impression that many statements in representation theory can be phrased a lot more elegantly using cohomological language. Therefore I'm trying to understand a bit better the sheaf theoretic framework for representation theory. To be specific I'd like to understand, for example, the purely formal parts (no hard "real" theorems) of the following ideas:

• Induction and Coinduction as different pushforwards of sheaves

• Equivariant sheaves as sheaves on quotient stacks and relation to the (Co-)induction functors.

I have some background in algebraic geometry and homological algebra (i'm even fine with some moderate stacky language) so I think I have the nessasary tools to understand this yet unfortunately I'm having a hard time finding references for statements appearing, for example, in the answers to the following question.

Is there a source that tells the overall cohomological story of representation theory with some sketches of proofs for the obviously formal propositions? (for example that thing with induction and pushforward which looks entirely formal to me).

By now I have the impression that many statements in representation theory can be phrased a lot more elegantly using cohomological language. Therefore I'm trying to understand a bit better the sheaf theoretic framework for representation theory. To be specific I'd like to understand, for example, the purely formal parts (no hard "real" theorems) of the following ideas:

• Induction and Coinduction as different pushforwards of sheaves

• Equivariant sheaves as sheaves on quotient stacks and relation to the (Co-)induction functors.

I have some background in algebraic geometry and homological algebra (i'm even fine with some moderate stacky language) so I think I have the nessasary tools to understand this yet unfortunately I'm having a hard time finding references for statements appearing, for example, in the answers to the following question.

Is there a source that tells the overall cohomological story of representation theory with some sketches of proofs for the obviously formal propositions? (for example that thing with induction and pushforward which looks entirely formal to me).

By now I have the impression that many statements in representation theory can be phrased a lot more elegantly using cohomological language. Therefore I'm trying to understand a bit better the sheaf theoretic framework for representation theory. To be specific I'd like to understand, for example, the purely formal parts (no hard "real" theorems) of the following ideas:

• Induction and Coinduction as different pushforwards of sheaves

• Equivariant sheaves as sheaves on quotient stacks and relation to the (Co-)induction functors.

I have some background in algebraic geometry and homological algebra (i'm even fine with some moderate stacky language) so I think I have the nessasary tools to understand this yet unfortunately I'm having a hard time finding references for statements appearing, for example, in the answers to the following question.

Is there a source that tells the cohomological story of representation theory with some sketches of proofs for the obviously formal propositions? (for example that thing with induction and pushforward which looks entirely formal to me).

By now I have the impression that many statements in representation theory can be phrased a lot more elegantly using cohomological language. Therefore I'm trying to understand a bit better the sheaf theoretic framework for representation theory. To be specific I'd like to understand, for example, the purely formal parts (no hard "real" theorems) of the following ideas:

• Induction and Coinduction as different pushforwards of sheaves

• Equivariant sheaves as sheaves on quotient stacks and relation to the (Co-)induction functors.

I have some background in algebraic geometry and homological algebra (i'm even fine with some moderate stacky language) so I think I have the nessasary tools to understand this yet unfortunately I'm having a hard time finding references for statements appearing, for example, in the answers to the following question.

Is there a source that tells the overall cohomological story of representation theory with some sketches of proofs for the obviously formal propositions? (for example that thing with induction and pushforward which looks entirely formal to me).