Geometric realizations of Lusztig's symmetries

2015/01/08 by Jie Xiao, Minghui Zhao, Xiao, Jie +1 · 2 citations
Mathematics · #16G20 #17B37 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math.QA #math.RT #msc:16G20 #msc:17B37

paper · pdf · doi:10.48550/arxiv.1501.01778

openalex publication_date 2015/01/08 · arxiv created 2015/01/24 · arxiv updated 2015/01/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• 2-Kac-Moody algebras

Cited by

• Ringel-Hall algebras beyond their quantum groups I: Restriction functor and Green's formula
• Geometric realizations of Lusztig's symmetries of symmetrizable quantum groups

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