3 problems

The main conjecture. (a) The set

Let $q$ be odd, let $n=2m$, and write $U_n=\mathrm{U}(n, {\mathbb F}_{q^2})$. Let $\tau$ be the transpose-inverse automorphism, let $y\tau$ be an element of the split extension…

Let $q$ be odd, let $m$ be a positive integer, and let $\mathrm{U}(2m, {\mathbb F}_{q^2})$ be the finite unitary group. A semisimple symplectic character is an irreducible complex…