arXiv subjects

Jingmin Guo

Publications and source records attributed to Jingmin Guo.

3 recordsLinked to original sources

arXiv2025

Langlands branching rule for type B snake modules

We prove that each snake module of the quantum Kac-Moody algebra of type $B_n^{(1)}$ admits a Langlands dual representation, as conjectured by Frenkel and Hernandez (Lett. Math. Phys. (2011) 96:217-261). Furthermore, we establish an explicit formula, called the Langlands branching rule, which gives the multiplicities in the decomposition of the character of a snake module of the quantum Kac-Moody algebra of type $B_n^{(1)}$ into a sum of characters of irreducible representations of its Langlands dual algebra.

math.RT↗

arXiv2025

Maximal green sequences for $\mathcal{Q}^N$ quivers

We introduce $\mathcal{Q}^N$ quivers and construct maximal green sequences for these quivers. We prove that any finite connected full subquiver of the quivers defined by Hernandez and Leclerc, arising in monoidal categorifications of cluster algebras, is a special case of $\mathcal{Q}^N$ quivers. Moreover, we prove that the trees of oriented cycles introduced by Garver and Musiker are special cases of $\mathcal{Q}^N$ quivers. This result resolves an open problem proposed by Garver and Musiker, providing a construction of maximal green sequences for quivers that are trees of oriented cycles. Furthermore, we prove that quivers that are mutation equivalent to an orientation of a type AD Dynkin diagram can also be recognized as special cases of $\mathcal{Q}^N$ quivers.

math.AC↗

arXiv2023

Generalized Hernandez-Leclerc modules and cluster algebras

We introduce generalized Hernandez-Leclerc modules over $U_q(\widehat{\mathfrak{sl}_{n+1}})$ as a generalization of Hernandez-Leclerc modules of type A, and prove that they are real and prime via monoidal categorifications of cluster algebras.

math.QA↗