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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeNov 7th 2013
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   Author: Urs
   Format: MarkdownItexI have split off _[[group character]]_ from _[[character]]_ and added discussion of how character groups of tori are isomorphic to their fundamental group. What happens to this statement for more general ellitpic curves?

   I have split off group character from character and added discussion of how character groups of tori are isomorphic to their fundamental group.

   What happens to this statement for more general ellitpic curves?

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeJan 31st 2022
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   Author: Urs
   Format: MarkdownItexJust trivia, but maybe somebody can help me out with a pointer: The character group $Hom\big(G,U(1)\big)$ acts on the collection of $G$-representations by tensoring, in paricular it acts on the set of irreps, and on the set underlying the representation ring. That's trivial, but it's nevertheless important. What's a canonical textbook that would state this action explicitly, and maybe have some commentary on it? I feel a little silly for asking this, but have had trouble finding much of a reference at all. David C. kindly points out that it's at least mentioned on [p. 12](https://arxiv.org/pdf/1512.03811.pdf#page=12) of [arXiv:1512.03811](https://arxiv.org/abs/1512.03811), but one would hope for a more canonical reference. I feel like I might just be lacking the right search term to go for?

   Just trivia, but maybe somebody can help me out with a pointer:

   The character group $Hom\big(G,U(1)\big)$ acts on the collection of $G$-representations by tensoring, in paricular it acts on the set of irreps, and on the set underlying the representation ring.

   That’s trivial, but it’s nevertheless important. What’s a canonical textbook that would state this action explicitly, and maybe have some commentary on it?

   I feel a little silly for asking this, but have had trouble finding much of a reference at all. David C. kindly points out that it’s at least mentioned on p. 12 of arXiv:1512.03811, but one would hope for a more canonical reference.

   I feel like I might just be lacking the right search term to go for?