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May 8, 2016 at 16:13 comment added Mike B Try section 3 of the "Introduction to the Trace Formula." For example, $\mathrm{GL}(N,\mathbb{A})^1$ is the subgroup of matrices whose determinant has absolute value 1.
May 7, 2016 at 0:29 comment added Alex Youcis Hey Mike. Thanks for the answer! It'll take me a day or so to process it/look up these references. One in the interim: what is $G(\mathbb{A})^1$? The only definition I can think of seems like it would depend on a choice of a faithful representation of $G$. Moreover, I have not seen anyone discuss eschewing the central character using this $G(\mathbb{A})^1$. Do you have a reference?
May 5, 2016 at 14:47 history answered Mike B CC BY-SA 3.0