Shaolong Han

activity

20242026

collaborators

4 papers

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.QA2024

Perfect basis theory for quantum Borcherds-Bozec algebras

Zhaobing Fan, Shaolong Han, Seok-Jin Kang +1

In this paper, we develop the perfect basis theory for quantum Borcherds-Bozec algebras $U_{q} (g)$ and their irreducible highest weight modules $V (λ)$ . We show that the l…

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

Perfect basis theory for quantum Borcherds-Bozec algebras

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