Shaolong Han

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20222026

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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.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…

Perfect basis theory for quantum Borcherds-Bozec algebras

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

Differential operator approach to quantum groups and their oscillator representations

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

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