Expanding the classical work of Kazhdan-Lusztig, we construct a bar involution and canonical bases on the q-Brauer algebra introduced by Wenzl. We define explicit actions of the q-Brauer algebra on the tensor spaces, and formulate ıSchur dualities between the q-Brauer algebra and the ıquantum groups of type AI and AII respectively. CONTENTS 1. Introduction 1 2. q-Brauer algebras 3 3. A bar involution and canonical bases 6 4. ıSchur duality of type AI 12 5. ıSchur duality of type AII 17 References 22
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