Finite-dimensional irreducible modules of the universal Askey–Wilson algebra at roots of unity

Let F denote an algebraically closed field and assume that q ? is a primitive d th root of unity with ? 1 , 2 4 . The universal Askey–Wilson algebra ? unital associative -algebra defined by generators relations. are A B C the relations assert each + ? commutes We show every finite-dimensional irreducible -module dimension less than or equal to { if odd ; / even Moreover we provide example bound tight.