Shaolong Han

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20242026

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math.RT2026

Closed formulas for energy functions on tensor squares of higher-level perfect crystals in classical affine types

Shaolong Han

For every $l \geq 1$ , we construct explicit closed-form coordinate formulas for the local energy functions on the tensor products $B_{l} \otimes B_{l}$ of level- $l$ perfect crystals in cl…

math.RT2026

Young tableau descriptions for the polyhedral realizations of crystal bases in type $A_{n}$

Shaolong Han

By utilizing the combinatorial properties of various tableau models, we establish an explicit correspondence between the polyhedral realizations of the crystal bases $\mathcal B(λ)…

math.RT2025

Rogers-Ramanujan type identities at $Λ_{0}$ from perfect crystals of exceptional quantum affine algebras

Shaolong Han

We derive Rogers--Ramanujan type partition identities at the fundamental weight $Λ_{0}$ for the exceptional affine types $G_{2}^{(1)}$ , $D_{4}^{(3)}$ , $F_{4}^{(1)}$ , $E_{6}^{(2)}$ , $E_6^{(1)…

math.RT2024

Young wall models for the level 1 highest weight and Fock space crystals of $U_{q} (E_{6}^{(2)})$ and $U_{q} (F_{4}^{(1)})$

Shaolong Han, Yuanfeng Jin, Seok-Jin Kang +1

In this paper we construct Young wall models for the level $1$ highest weight and Fock space crystals of quantum affine algebras in types $E_{6}^{(2)}$ and $F_{4}^{(1)}$ . Our starting…

math.RT2023

Differential operator realization of braid group action on $$ quantum groups

Zhaobing Fan, Jicheng Geng, Shaolong Han

We construct a unique braid group action on modified $q$ -Weyl algebra $A_{q} (S)$ . Under this action, we give a realization of the braid group action on quasi-split $$ qu…

Closed formulas for energy functions on tensor squares of higher-level perfect crystals in classical affine types

Young tableau descriptions for the polyhedral realizations of crystal bases in type An​

Rogers-Ramanujan type identities at Λ0​ from perfect crystals of exceptional quantum affine algebras

Young wall models for the level 1 highest weight and Fock space crystals of Uq​(E6(2)​) and Uq​(F4(1)​)

Differential operator realization of braid group action on quantum groups

Young tableau descriptions for the polyhedral realizations of crystal bases in type $A_{n}$

Rogers-Ramanujan type identities at $Λ_{0}$ from perfect crystals of exceptional quantum affine algebras

Young wall models for the level 1 highest weight and Fock space crystals of $U_{q} (E_{6}^{(2)})$ and $U_{q} (F_{4}^{(1)})$

Differential operator realization of braid group action on $$ quantum groups