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Geometric construction of crystal bases for quantum generalized Kac-Moody algebras
Seok-Jin Kang, Masaki Kashiwara, Olivier Schiffmann
We provide a geometric realization of the crystal for quantum generalized Kac-Moody algebras in terms of the irreducible components of certain Lagrangian subvarieties i…
Crystal bases of the Fock space representations and string functions
Seok-Jin Kang, Jae-Hoon Kwon
Let a the quantum affine algebra of type , , , , and , and let be th…
Canonical bases for quantum generalized Kac-Moody algebra
Seok-Jin Kang, Olivier Schiffmann
We construct a canonical basis for quantum generalized Kac-Moody algebra via semisimple perverse sheaves on varieties of representations of quivers. We compare this basis with the…
Higher level affine crystals and Young walls
Seok-Jin Kang, Hyeonmi Lee
Using combinatorics of Young walls, we give a new realization of arbitrary level irreducible highest weight crystals for quantum affine algebras of type $A_n^{(1)}…
Young Wall Realization of Crystal Bases for Classical Lie Algebras
Seok-Jin Kang, Jeong-Ah Kim, Hyeonmi Lee +1
In this paper, we give a new realization of crystal bases for finite dimensional irreducible modules over classical Lie algebras. The basis vectors are parameterized by certain You…
Crystal Bases for Quantum Generalized Kac-Moody Algebras
Kyeonghoon Jeong, Seok-Jin Kang, Masaki Kashiwara
In this paper, we develop the crystal basis theory for quantum generalized Kac-Moody algebras. For a quantum generalized Kac-Moody algebra , we first introduce th…