1 citations · 1 across the 10 of their papers we have counts for
10 papers
Double Hall-Littlewood symmetric polynomials
Jiayi Chen, Ming Lu, Shiquan Ruan
We establish a ring isomorphism between the derived Hall algebra of the Jordan quiver and the ring of double symmetric functions (i.e., the ring of symmetric polynomials in two set…
iQuantum groups and iHopf algebras II: dual canonical bases
Jiayi Chen, Ming Lu, Xiaolong Pan +2
Building on the iHopf algebra realization of quasi-split universal iquantum groups developed in a prequel, we construct the dual canonical basis for a universal iquantum group of a…
iQuantum groups and iHopf algebras I: foundation
Jiayi Chen, Ming Lu, Xiaolong Pan +2
We introduce the notion of iHopf algebra, a new associative algebra structure defined on a Hopf algebra equipped with a Hopf pairing. The iHopf algebra on a Borel quantum group end…
Small-Large Collaboration: Training-efficient Concept Personalization for Large VLM using a Meta Personalized Small VLM
Sihan Yang, Huitong Ji, Shaolin Lu +6
Personalizing Vision-Language Models (VLMs) to transform them into daily assistants has emerged as a trending research direction. However, leading companies like OpenAI continue to…
Hopf algebras associated with self-dual Hopf algebras
Jiayi Chen, Shiquan Ruan
Motivated by the construction of Hall algebras and -Hall algebras, we introduce Hopf algebras associated with symmetrically self-dual Hopf algebras. We prove tha…
Hall Polynomials for Weighted projective lines
Jiayi Chen, Bangming Deng, Shiquan Ruan
This paper deals with the triangle singularity defined by the \linebreak equation for weight triple , as well as the category of co…
Derived Hall algebras of root categories
Jiayi Chen, Ming Lu, Shiquan Ruan
For a finitary hereditary abelian category , we define a derived Hall algebra of its root category by counting the triangles and using the octahedral axiom, which is p…
New realization of quantum groups via -Hall algebras
Jiayi Chen, Yanan Lin, Shiquan Ruan
For an essentially small hereditary abelian category , we define a new kind of algebra , called the -Hall algebra of . The…
Frobenius-Perron theory of representation-directed algebras
J. M. Chen, J. Y. Chen
We study the Frobenius-Perron dimension of representation-directed algebras and quotient algebras of canonical algebras of type ADE, prove that the Frobenius-Perron dimension of a…
quantum groups of split type via derived Hall algebras
Jiayi Chen, Ming Lu, Shiquan Ruan
A quantum symmetric pair consists of a quantum group and its coideal subalgebra (called an quantum group) with parameters…