We study the representation theory of the quantum queer superalgebra Uₕ ({q₍) } and obtain some properties of the highest weight modules. Furthermore, based on the realization of Uₕ ({q₍) }, we study the representation theory of the twisted queer q-Schur superalgebra {{Q}ₕ (n, r) }, and obtain the decomposition of its regular module as a direct sum of irreducible submodules, which also means {{Q}ₕ (n, r) } is semisimple.
Zhenhua Li (Thu,) studied this question.