Timeline for Reference needed for representation theory of direct products of algebraic groups over a field (of arbitrary characteristic)
Current License: CC BY-SA 3.0
4 events
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| Nov 10, 2011 at 22:10 | comment | added | Mike Crumley | I think there is a great deal of confusion concerning notation (which is my fault, I apologize). I will try to reformulate the question in terms of comodules over the representing Hopf algebras of the groups. | |
| Nov 10, 2011 at 18:07 | comment | added | Chuck Hague | I agree, I don't think it's true even in the case that the $G \times H$-representation is indecomposable. My guess is that the following statement is true: Any representation of $G \times H$ has a filtration with subquotients isomorphic to modules of the form $V \otimes W$. | |
| Nov 10, 2011 at 17:39 | comment | added | David Jordan | Perhaps the OP meant to consider only irreducible representations of $G\times H$? With the appropriate assumptions, every irreducible representation of $G\times H$ is obtained as an external product of irreducibles of $G$ and $H$. However, I think it's not true in general, even if you restrict to indecomposables of $G\times H$. | |
| Nov 10, 2011 at 17:29 | history | answered | Chuck Hague | CC BY-SA 3.0 |