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math.RT2025
Structure coefficients for quantum groups
Yixin Lan, Yumeng Wu, Jie Xiao
According to the Hall algebras of quivers with automorphisms under Lusztig's construction, the polynominal forms of several structure coefficients for quantum groups of all finite…
math.RT2025
Lusztig sheaves, decomposition rule and restriction rule
Yixin Lan
In this article, we realize the subquotient based modules of certain tensor products or restricted modules via Lusztig's perverse sheaves on multi-framed quivers, and provide a con…
math.RT2025
Lusztig sheaves, characteristic cycles and the Borel-Moore homology of Nakajima's quiver varieties
Jiepeng Fang, Yixin Lan
By using characteristic cycles, we build a morphism from the canonical bases of integrable highest weight modules of quantum groups to the top Borel-Moore homology groups of Nakaji…