Jae-Hoon Kwon

Kostant homology formulas for oscillator modules of Lie superalgebras

Abstract We provide a systematic approach to obtain formulas for characters and Kostant u -homology groups of the oscillator modules of the finite-dimensional general linear and ortho-symplectic superalgebras, via Howe dualities for infinite-dimensional Lie algebras. Specializing these Lie superalgebras to Lie algebras, we recover, in a new way, formulas for Kostant homology groups of unitarizable highest weight representations of Hermitian symmetric pairs. In addition, two new reductive dual pairs related to the above-mentioned u -homology computation are worked out.

Super Duality and Crystal Bases for Quantum Ortho-Symplectic Superalgebras

Let

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

\mathcal{O}^{int}_q(m|n)

Finite-Dimensional Half-Integer Weight Modules over Queer Lie Superalgebras

be a semisimple tensor category of modules over a quantum ortho-symplectic superalgebra of type

Howe Duality and Kostant Homology Formula for Infinite-Dimensional Lie Superalgebras

B, C, D

Peterson-type dimension formulas for graded Lie superalgebras

introduced in the authors previous work. It is a natural counterpart of the category of finitely dominated integrable modules over a quantum group of type

Character Formulae for Queer Lie Superalgebras and Canonical Bases of Types A / C

B, C, D

Kac–Wakimoto character formula for ortho-symplectic Lie superalgebras

from a viewpoint of super duality. Continuing the previous work on type

Irreducible characters of Kac–Moody Lie superalgebras

B

Crystal Graphs and the Combinatorics of Young Tableaux

and