Seok-Jin Kang

Categorification of highest weight modules via Khovanov-Lauda-Rouquier algebras

In this paper, we prove Khovanov-Lauda’s cyclotomic categorification conjecture for all symmetrizable Kac-Moody algebras. Let

Crystal bases for quantum generalized kac¿moody algebras

U_{q}(\mathfrak{g})

Kac-Moody Lie algebras, spectral sequences, and the Witt formula

be the quantum group associated with a symmetrizable Cartan datum and let V(Λ) be the irreducible highest weight

Simplicity of heads and socles of tensor products

U_{q}(\mathfrak{g})

Level 1 perfect crystals and path realizations of basic representations at q = 0

-module with a dominant integral highest weight Λ. We prove that the cyclotomic Khovanov-Lauda-Rouquier algebra RΛ gives a categorification of V(Λ).

Dimension formula for graded Lie algebras and its applications

In this paper, we develop the crystal basis theory for quantum generalized Kac?Moody algebras. For a quantum generalized Kac?Moody algebra

On the centre of two-parameter quantum groups

U_q(\mathfrak{g})

Rank 2 symmetric hyperbolic Kac-Moody algebras

, we first introduce the category

CATEGORIFICATION OF QUANTUM GENERALIZED KAC–MOODY ALGEBRAS AND CRYSTAL BASES

\mathcal{O}_{int}

FOCK SPACE REPRESENTATIONS OF QUANTUM AFFINE ALGEBRAS AND GENERALIZED LASCOUX-LECLERC-THIBON ALGORITHM

of