Seok-Jin Kang

activity

19972022

most citedCategorification of Highest Weight Modules via Khovanov-Lauda-Rouquier Algebras

114 citations · 510 across the 61 of their papers we have counts for

collaborators

65 papers

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.QA2021

Global bases for quantum Borcherds-Bozec algebras

Zhaobing Fan, Seok-Jin Kang, Young Rock Kim +1

We provide a construction of global bases for quantum Borcherds-Bozec algebras and their integrable highest weight representations.

math.RT2020

Abstract crystals for quantum Borcherds-Bozec algebras

Zhaobing Fan, Seok-Jin Kang, Young Rock Kim +1

In this paper, we develop the theory of abstract crystals for quantum Borcherds-Bozec algebras. Our construction is different from the one given by Bozec. We further prove the crys…

math.RT2020

Classical limit of quantum Borcherds-Bozec algebras

Zhaobing Fan, Seok-Jin Kang, Young-Rock Kim +1

Let $g$ be a Borcherds-Bozec algebra, $U (g)$ be its universal enveloping algebra and $U_{q} (g)$ be the corresponding quantum Borcherds-Bozec algebr…

math.RT2019

Quantum Borcherds-Bozec algebras and their integrable representations

Seok-Jin Kang, Young-Rock Kim

We investigate the fundamental properties of quantum Borcherds-Bozec algebras and their representations. Among others, we prove that the quantum Borcherds-Bozec algebras have a tri…