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pro vyhledávání: '"Fang, Jiepeng"'
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 the trace map. In this paper, we generalize their formula to that for
Externí odkaz:
http://arxiv.org/abs/2406.03238
Autor:
Fang, Jiepeng
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 of quiver representations is a Lusztig's perverse sheaf if and only if
Externí odkaz:
http://arxiv.org/abs/2401.02770
Autor:
Fang, Jiepeng, Lan, Yixin
By introducing $N$-framed quivers, we define the localization of Lusztig's sheaves for $N$-framed quivers and functors $E^{(n)}_{i}, F^{(n)}_{i}, K^{\pm}_i$ for localizations. This gives a categorical realization of tensor products of integrable high
Externí odkaz:
http://arxiv.org/abs/2310.18682
We consider the localization $\mathcal{Q}_{\mathbf{V},\mathbf{W}}/\mathcal{N}_{\mathbf{V}}$ of Lusztig's sheaves for framed quivers, and define functors $E^{(n)}_{i},F^{(n)}_{i},K^{\pm}_{i},n\in \mathbb{N},i \in I$ between the localizations. With the
Externí odkaz:
http://arxiv.org/abs/2307.16131
Let $A$ be a finite-dimensional $\mathbb{C}$-algebra of finite global dimension and $\mathcal{A}$ be the category of finitely generated right $A$-modules. By using of the category of two-periodic projective complexes $\mathcal{C}_2(\mathcal{P})$, we
Externí odkaz:
http://arxiv.org/abs/2305.06664
As one of results in [6], Bridgeland realized the quantum group $\mathrm{U}_v(\mathfrak{g})$ via the localization of Ringel-Hall algebra for two-periodic projective complexes of quiver representations over a finite field. In the present paper, we gen
Externí odkaz:
http://arxiv.org/abs/2303.04993
Given any symmetric Cartan datum, Lusztig has provided a pair of key lemmas to construct the perverse sheaves over the corresponding quiver and the functions of irreducible components over the corresponding preprojective algebra respectively. In the
Externí odkaz:
http://arxiv.org/abs/2210.16758
Publikováno v:
In Advances in Mathematics November 2024 456
Our investigation in the present paper is based on three important results. (1) In [12], Ringel introduced Hall algebra for representations of a quiver over finite fields and proved the elements corresponding to simple representations satisfy the qua
Externí odkaz:
http://arxiv.org/abs/2108.12595
Publikováno v:
In Journal of Algebra 15 March 2023 618:67-95