MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Let $G$ a split connected reductive group and $G(\mathbb{A})$ his points in the ring of adeles.

We have a degree map $G(\mathbb{A})\rightarrow X_{*}(Z)$ where $Z$ is the center of $G$.

Let $G(\mathbb{A})^{1}$ the degree zero elements and take an element $\gamma\in G(\mathbb{A})$

Do we have an isomorphism between $G_{\gamma}(\mathbb{A})^{1}\backslash G(\mathbb{A})^{1}$ and $G_{\gamma}(\mathbb{A})\backslash G(\mathbb{A})$ where $G_{\gamma}$ is the centralizer of $\gamma$?

share|cite|improve this question
If the restriction of the degree map to the center surjects, then I'd think the answer is yes! e.g. Gl(n) and sl(n). – Marc Palm Feb 19 '13 at 7:17

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.