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Coxeter Transformations in Quantum Groups |
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| Authors: | Jie Xiao Shilin Yang |
| Institution: | (1) Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, China. e-mail;(2) Department of Mathematics, Beijing Polytechnic University, Beijing, 100022, China;(3) Department of Mathematics, Beijing Normal University, Beijing, 100875, China |
| Abstract: | It is natural to define a Coxeter transformation in quantum groups by the product of Lusztig's symmetries in some order. In this note, we show that the Ringel–Hall algebra approach enables us to determine the behavior of its action in case of finite type. |
| Keywords: | Ringel– Hall algebra quantum group Coxeter transformation |
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