arXiv subjects

Lingen Ding

Publications and source records attributed to Lingen Ding.

3 recordsLinked to original sources

arXiv2026

A common interleaver for two antichain polynomials on $[k]$$\times$ $P_{n,s}$

The first author and Dong \cite{DD} proposed three conjectures on antichain generating polynomials. Jiang \cite{Jiang} recently proved Conjectures 4.3 and 4.5, concerning real-rootedness and $γ$-positivity. We prove Conjecture 4.2 by adapting his method from $[k]\times [2] \times [n]$ to $[k]\times P_{n,s} $, where $P_{n,s}$ is a two-row Ferrers shape. We establish real stability for a family of bivariate polynomials associated with adjacent shapes, then apply the Chudnovsky-Seymour compatibility criterion to obtain a common interleaver. As noted in \cite{DD}, Conjecture 4.2 also implies Conjecture 4.3.

math.CO↗

arXiv2026

Derivations and local derivations on Euclidean Lie algebras

The present paper is devoted to studying derivations and local derivations on the Euclidean Lie algebras $\mathfrak{e}(n)$. We give a complete desrciption of the derivation algebra of $\mathfrak{e}(n)$ for $n\geq 4$. Furthermore, we prove that every local derivations on the $\mathfrak{e}(n)$ is a derivation.

math.RA↗

arXiv2023

Vertex algebras and TKK algebras

In this paper, we associate the TKK algebra $\widehat{\mathcal{G}}(\mathcal{J})$ with vertex algebras through twisted modules. Firstly, we prove that for any complex number $\ell$, the category of restricted $\widehat{\mathcal{G}}(\mathcal{J})$-modules of level $\ell$ is canonically isomorphic to the category of $σ$-twisted $V_{\widehat{\mathcal{C}_{\mathfrak g}}}(\ell,0)$-modules, where $V_{\widehat{\mathcal{C}_{\mathfrak g}}}(\ell,0)$ is a vertex algebra arising from the toroidal Lie algebra of type $C_2$ and $σ$ is an isomorphism of $V_{\widehat{\mathcal{C}_{\mathfrak g}}}(\ell,0)$ induced from the involution of this toroidal Lie algebra. Secondly, we prove that for any nonnegative integer $\ell$, the integrable restricted $\widehat{\mathcal{G}}(\mathcal{J})$-modules of level $\ell$ are exactly the $σ$-twisted modules for the quotient vertex algebra $L_{\widehat{\mathcal{C}_{\mathfrak g}}}(\ell,0)$ of $V_{\widehat{\mathcal{C}_{\mathfrak g}}}(\ell,0)$. Finally, we classify the irreducible $\frac{1}{2}{\mathbb{N}}$-graded $σ$-twisted $L_{\widehat{\mathcal{C}_{\mathfrak g}}}(\ell,0)$-modules.

math.QA↗