Relation between group representations and elements of group cohomology groups - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-25T04:15:27Z http://mathoverflow.net/feeds/question/36450 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/36450/relation-between-group-representations-and-elements-of-group-cohomology-groups Relation between group representations and elements of group cohomology groups David Corwin 2010-08-23T14:57:10Z 2010-08-23T14:57:10Z <p>Having already seen group cohomology, I was just introduced to the formula $U \otimes Ind W = Ind(Res(U) \otimes W)$ from representation theory. This seems oddly like the formula $\mathrm{Cor}(u) \cup v = \mathrm{Cor}(u \cup \mathrm{Res}(v))$, which can be found as Proposition 1.39 in Chapter 2 of <a href="http://www.jmilne.org/math/CourseNotes/CFT.pdf" rel="nofollow">Milne's CFT Notes</a>. Can one be proven from the other? In one case, $U, W$ are actual modules, whereas in the other case, $u,v$ are elements of modules. Maybe this means that certain $G$-modules might somehow classify representations, and the cup product would represent the tensor product of representations?</p>