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Jie Liu

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Preprint Sep 2026

Elementary modules of the generalized Kronecker quivers K(n)

Let $k$ be an algebraically closed field. The generalized or $n$-Kronecker quiver $K(n)$ is the quiver with two vertices, called a source and a sink, and $n$ arrows from source to sink. We use $\modd\cK_n$ to denote the category of the finite-dimensional modules of the path algebra $\cK_n=kK(n)$. There exist a function...

Jie Liu · 0 citations

Preprint Jul 2026

Quantitative Fourier Restriction Estimates for Weyl Operators: Fourier-Support Dependence and Lower Bounds

The Weyl calculus associates a function $a$ on phase space $\mathbb{R}^{2d}$ with the corresponding Weyl operator $L_a$ acting on $L^2(\mathbb{R}^d)$. At $p=2$, this correspondence is governed by an exact Hilbert--Schmidt identity. For $p\neq2$, two-sided $L^p$--Schatten estimates are known for Paley--Wiener type symbo...

Jie Liu · 0 citations