Cells in quantum affine sl_n
Kevin McGerty
TL;DR
This paper explores Lusztig's theory of cells within quantum affine sl_n, providing explicit descriptions and verifying conjectures using geometric constructions of quantum groups.
Contribution
It explicitly describes two-sided cells, counts left cells, and analyzes the asymptotic algebra in quantum affine sl_n, confirming Lusztig's conjectures.
Findings
Explicit description of two-sided cells
Quantification of left cells within two-sided cells
Verification of Lusztig's conjectures on asymptotic algebra
Abstract
We study Lusztig's theory of cells for quantum affine . 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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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Combinatorial Mathematics · Random Matrices and Applications