| Register
\(\newcommand{\Cat}{{\rm Cat}} \) \(\newcommand{\A}{\mathcal A} \) \(\newcommand{\freestar}{ \framebox[7pt]{$\star$} }\)

1. Representations

    1. Iwahori-Matsumoto presentation


      Add remark

      Problem 1.1.

      [M. Weissman] What is the “Iwahori-Matsumoto Presentation” of Iwahori-Hecke algebra for $\widetilde{G}_F$ for split $G_F$?


        • Add remark

          Problem 1.2.

          [W. Gan] Construct supercuspidal representations of $\widetilde{G}_{F}$.


            • Add remark

              Problem 1.3.

              [K. Choiy] What is the category of depth-zero unipotent representations for $\widetilde{G}_{F}$ for a $p$-adic field $F$?

                • Steinberg representation


                  Add remark

                  Problem 1.4.

                  [G. Savin] Define Steinberg representation of $\widetilde{G}_{F}$. What is the formal degree of Steinberg representation of $\widetilde{G}_{F}$ when $G$ is split over $F$?

                  What is analogue of the trivial representation?


                    • Add remark

                      Problem 1.5.

                      [W. Gan] What is theta correspondence for $\widetilde{G}$?

                      e.g.) $SL_2 \times \widetilde{SL}^{(3)}_2 \hookrightarrow \widetilde{G_2}^{(3)}$ (G-R-S)

                      $SL_3 \times \widetilde{SL}^{(2)}_3 \hookrightarrow \widetilde{F_4}^{(2)}$

                      $\widetilde{Spin}^{(2)}_{2a+1} \times \widetilde{Spin}^{(2)}_{2b} \hookrightarrow \widetilde{Spin}^{(2)}_{2(a+b)+1}$ (Loke-Savin)

                      $\widetilde{Spin}^{(2)}_{5} \times \widetilde{Spin}^{(2)}_{4} \hookrightarrow \widetilde{Spin}^{(2)}_{9}$

                          Cite this as: AimPL: Automorphic forms on covering groups, available at http://aimpl.org/autoformcovergp.