Geometric realizations of Lusztig's symmetries
Jie Xiao, Minghui Zhao
TL;DR
This paper provides geometric realizations of Lusztig's symmetries and constructs projective resolutions of standard modules, leading to a categorification of these symmetries' formulas.
Contribution
It introduces a novel geometric approach to realize Lusztig's symmetries and develops projective resolutions, advancing the categorification of quantum group symmetries.
Findings
Geometric realizations of Lusztig's symmetries achieved
Constructed projective resolutions of standard modules
Categorification of Lusztig's symmetry formulas obtained
Abstract
In this paper, we give geometric realizations of Lusztig's symmetries. We also give projective resolutions of a kind of standard modules. By using the geometric realizations and the projective resolutions, we obtain the categorification of the formulas of Lusztig's symmetries.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Advanced Algebra and Geometry