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Analysis explores representation theory and highest weight modules in quantum queer superalgebras, highlighting structural properties.
We study the representation theory of the quantum queer superalgebra U_v(qₙ) and obtain some properties of the highest weight modules. Furthermore, based on the realization of U_v(qₙ), we study the representation theory of the twisted queer q-Schur superalgebra Q_v(n,r), and obtain the decomposition of its regular module as a direct sum of irreducible submodules, which also means Q_v(n,r) is semisimple.
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Zhenhua Li (2025) studied this question.
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