5 problems

Let $m\geq 3$, and let $SC_m\rightarrow SL(V)$ be a representation satisfying the condition in. Write $d_V$ for the height (Dynkin index) of $V$, and let $N_{d_V}^{+}$ and…

In the cases labeled Case 4 and Cases 7 and 8, let $\pi$ denote the representation described in the surrounding case analysis. Splitting conjecture. Each such representation decomp…

Basic-case unitarity conjecture. The basic cases from which the unitary dual is obtained by unitary induction and complementary series should have $\pi_0$ unitary, and their infini…

Let $G(E_{10})$ be the split real Kac–Moody group of type $E_{10}$, let $K(E_{10})$ be the subgroup fixed by its Cartan–Chevalley involution, and let $\mathrm{Spin}(E_{10})$ be a d…

Let $p$ be an odd prime, let $q$ be a power of $p$, and let $\mathbb{F}_q$ be the finite field with $q$ elements. For $n\geq 3$, let $\mathrm{Spin}(n)$ be the spin group, let…