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Mathematics > Representation Theory

Title: Geometrizations of quantum groups and dual semicanonical bases

Authors: Yingjin Bi
(Submitted on 31 Mar 2024 (v1), last revised 26 Apr 2024 (this version, v2))
Abstract: In this paper, we give a geometrization of semicanonical bases of quantum groups via Grothendieck groups of the derived categories of Lusztig's nilpotent varieties. Meanwhile, we describe the dual semicanonical bases in terms of Serre polynomials of Grassmannians of modules over preprojective algebras.
Comments: 10 pages. Any comments welcome
Subjects: Representation Theory (math.RT); Algebraic Geometry (math.AG); Quantum Algebra (math.QA); Rings and Algebras (math.RA)
MSC classes: 17B37, 16G20, 20G42
Cite as: arXiv:2404.00663 [math.RT]
  (or arXiv:2404.00663v2 [math.RT] for this version)

Submission history

From: Yingjin Bi [view email]
[v1] Sun, 31 Mar 2024 12:15:16 GMT (14kb)
[v2] Fri, 26 Apr 2024 00:54:59 GMT (15kb)
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