7 papers
Thickening realization and positivity properties of canonical bases
Jiepeng Fang, Xuhua He
Let be a quantum group associated with a symmetric Cartan datum, let be its modified form, and let be the canonical basis of $\do…
Canonical bases of tensor products and positivity properties
Jiepeng Fang, Xuhua He
Let be a quantum group of symmetric type. We introduce the {\it thickening realization} to realize (a suitable approximation of) the tensor product ${^ωΛ_{λ_1}}\otimes…
Canonical bases of tensor products of integrable highest weight modules arising from framed constructions
Jiepeng Fang, Yixin Lan
Given a quantum group, we prove that the canonical bases of the tensor products of its integrable highest weight modules can be obtained from the canonical bases of the integrable…
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…
The parity of Lusztig's restriction functor and Green's formula for a quiver with automorphism
Jiepeng Fang, Yixin Lan, Yumeng Wu
In [8], Fang-Lan-Xiao proved a formula about Lusztig's induction and restriction functors which can induce Green's formula for the path algebra of a quiver over a finite field via…
On singular supports of Lusztig's perverse sheaves
Jiepeng Fang
We prove a conjecture of Lusztig on a microlocal characterization of his perverse sheaves. For any finite quiver without loops, an equivariant simple perverse sheaf on the variety…