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The representations of quantized walled Brauer algebras. (English) Zbl 1358.20007

Summary: In this paper, we give a criterion on the semisimplicity of quantized walled Brauer algebras \(\mathcal{B}_{r, s}\) and classify its simple modules over an arbitrary field \(\kappa\).

MSC:

20C08 Hecke algebras and their representations
17B37 Quantum groups (quantized enveloping algebras) and related deformations
20G43 Schur and \(q\)-Schur algebras
16S99 Associative rings and algebras arising under various constructions
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