Geometric realizations of Lusztig's symmetries on the whole quantum groups
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lusztiggeometricgroupquantumrealizationssymmetriesdecompositiongive
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In this paper, we shall study the structure of the Grothendieck group of the category consisting of Lusztig's perverse sheaves and give a decomposition theorem of it. By using this decomposition theorem and the geometric realizations of Lusztig's symmetries on the positive part of a quantum group, we shall give geometric realizations of Lusztig's symmetries on the whole quantum group.
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