### Bernstein's Lectures on Eisenstein Series: Questions on Lecture 1

They are linked from the following page:

http://www.math.uchicago.edu/~arinkin/langlands/

Questions on Lecture 1

1. What is meant by the last sentence in the remark on p. 2? In particular, what does the notation $f_{\lambda}=\exp(\lambda,j)$, where $j$ is $j$-invariant" mean?

2. What does Section 4. reduce to in the case of SL(2,R)?

3. What is the modified action of $L_p$ on $F(y_p)$ in the SL(2,R) case?

4. What does $Z(L_p)\supset Z(G)$ look like concretely in the case of $G=SL(n,R) and $P$ a standard parabolic?

5. Why does reduction theory imply the Proposition on p. 7?

http://www.math.uchicago.edu/~arinkin/langlands/

Questions on Lecture 1

1. What is meant by the last sentence in the remark on p. 2? In particular, what does the notation $f_{\lambda}=\exp(\lambda,j)$, where $j$ is $j$-invariant" mean?

2. What does Section 4. reduce to in the case of SL(2,R)?

3. What is the modified action of $L_p$ on $F(y_p)$ in the SL(2,R) case?

4. What does $Z(L_p)\supset Z(G)$ look like concretely in the case of $G=SL(n,R) and $P$ a standard parabolic?

5. Why does reduction theory imply the Proposition on p. 7?

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