Cells in quantum affine sl_n
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cellslusztigquantumaffinealgebraasymptoticcellconjectures
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We study Lusztig's theory of cells for quantum affine $\mathfrak{sl}_n$. Using the geometric construction of the quantum group due to Lusztig and Ginzburg--Vasserot, we describe explicitly the two-sided cells, the number of left cells in a two--sided cell, and the asymptotic algebra, verifying conjectures of Lusztig.
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