
## 1. Representations

1. ### Iwahori-Matsumoto presentation

#### Problem 1.1.

[M. Weissman] What is the “Iwahori-Matsumoto Presentation” of Iwahori-Hecke algebra for $\widetilde{G}_F$ for split $G_F$?
• #### Problem 1.2.

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

#### 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?
• #### 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.