Entropy bounds and quantum unique ergodicity for Hecke eigenfunctions on division algebras

Lior Silberman, Akshay Venkatesh

We prove the arithmetic quantum unique ergodicity (AQUE) conjecture for non-degenerate sequences of Hecke eigenfunctions on quotients $\Gamma \backslash G/K$, where $G\simeq\mathrm{PGL}_…