Shaolong Han

activity

20222026

collaborators

10 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…

math.QA2024

A new Young wall realization of $B (λ)$ and $B (\infty)$

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

Using new combinatorics of Young walls, we give a new construction of the arbitrary level highest weight crystal $B (λ)$ for the quantum affine algebras of types $A_{2 n}^{(2)}$ , $D^…

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…

math.RT2022

Young wall construction of level-1 highest weight crystals over $U_{q} (D_{4}^{(3)})$ and $U_{q} (G_{2}^{(1)})$

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

With the help of path realization and affine energy function, we give a Young wall construction of level-1 highest weight crystals $B (λ)$ over $U_{q} (G_{2}^{(1)})$ and $U_{q}(D_{4}…

math.RT2022

Crystal bases and canonical bases for quantum Borcherds-Bozec algebras

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

Let $U_{q}^{-} (g)$ be the negative half of a quantum Borcherds-Bozec algebra $U_{q} (g)$ and $V (λ)$ be the irreducible highest weight module with $λ \in P^{+}$ . I…

math.QA2022

Differential operator approach to $$ quantum groups and their oscillator representations

Zhaobing Fan, Jicheng Geng, Shaolong Han

For a quasi-split Satake diagram, we define a modified $q$ -Weyl algebra, and show that there is an algebra homomorphism between it and the corresponding $$ quantum group. In o…

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

A new Young wall realization of B(λ) and B(∞)

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 wall construction of level-1 highest weight crystals over Uq​(D4(3)​) and Uq​(G2(1)​)

Crystal bases and canonical bases for quantum Borcherds-Bozec algebras

Differential operator approach to quantum groups and their oscillator representations

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

A new Young wall realization of $B (λ)$ and $B (\infty)$

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

Young wall construction of level-1 highest weight crystals over $U_{q} (D_{4}^{(3)})$ and $U_{q} (G_{2}^{(1)})$

Differential operator approach to $$ quantum groups and their oscillator representations