Timeline for Definitions of $\pi_1 \times \pi_2, \pi_1 \boxplus \pi_2, \pi_1 \boxtimes \pi_2$
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| Apr 13, 2022 at 2:03 | comment | added | Seven | I was confused because in the line just before that you said "$\pi_1 \boxtimes \pi_2$ ought to denote a representation of the product of groups $\mathrm{GL}_{n_1}(F) \times \mathrm{GL}_{n_2}(F)$" and I can't reconcile the two. Maybe I'm missing something obvious here. | |
| Apr 13, 2022 at 1:53 | comment | added | Peter Humphries | @Seven No, the resulting representation is a representation of $\mathrm{GL}_{n_1 n_2}(F)$. | |
| Apr 13, 2022 at 1:52 | comment | added | Seven | When you describe $\boxtimes$ as a map from $\mathcal{R}(\mathrm{GL}_{n_1}(F)) \times \mathcal{R}(\mathrm{GL}_{n_2}(F))$, shouldn't the target be $\mathcal{R}(\mathrm{GL}_{n_1}(F) \times \mathrm{GL}_{n_2}(F))$? | |
| Jun 28, 2021 at 16:14 | history | edited | Peter Humphries | CC BY-SA 4.0 |
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| Aug 4, 2020 at 1:52 | history | edited | Peter Humphries | CC BY-SA 4.0 |
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| Jun 11, 2018 at 18:38 | comment | added | D_S | This is an excellent answer, thank you. When we are talking about the representation $\pi_1 \boxplus \pi_2$ of $\operatorname{GL}_{n_1+n_2}(F)$, is there a more precise statement of which "suitable irreducible subquotient" of $\textrm{Ind}_{MN}^{\textrm{GL}_{n_1+n_2}(F)} \pi_1 \boxtimes \pi_2$ is meant? | |
| Jun 11, 2018 at 18:34 | vote | accept | D_S | ||
| Jun 11, 2018 at 15:16 | comment | added | GH from MO | For Rankin-Selberg $L$-functions, there is also a nice summary in the Appendix of Rudnick-Sarnak: Zeros of principal $L$-functions and random matrix theory (see projecteuclid.org/euclid.dmj/1077245671). | |
| Jun 11, 2018 at 14:59 | history | edited | Peter Humphries | CC BY-SA 4.0 |
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| Jun 11, 2018 at 13:59 | history | answered | Peter Humphries | CC BY-SA 4.0 |