Seok-Jin Kang

collaborators

5 papers

math.RT2024

Categorification of quantum Borcherds-Bozec algebras

Seok-Jin Kang, Young Rock Kim, Bolun Tong

We categorify the quantum Borcherds-Bozec algebras by constructing their associated Khovanov-Lauda-Rouquier algebras.

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.RT2024

Highest weight modules over Borcherds-Bozec superalgebras and their character formula

Zhaobing Fan, Jiaqi Huang, Seok-Jin Kang +1

We present and prove the Weyl-Kac type character formula for the irreducible highest weight modules over Borcherds-Bozec superalgebras with dominant integral highest weights.

Categorification of quantum Borcherds-Bozec 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)​)

Highest weight modules over Borcherds-Bozec superalgebras and their character formula

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 $U_{q} (F_{4}^{(1)})$