Shaolong Han

activity

20222026

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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…

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 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