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6 papers · 1 filter
Quantum Cohomology Rings of Lagrangian and Orthogonal Grassmannians and Total Positivity
Daewoong Cheong
We verify in an elementary way a result of Peterson for the maximal orthogonal and Lagrangian Grassmannians, and then find Vafa-Intriligator type formulas which compute their 3-poi…
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…
Associative conformal algebras with finite faithful representation
Pavel Kolesnikov
We describe all irreducible conformal subalgebras of Cend_N. The classification of simple and semisimple associative conformal algebras with finite faithful representation follows…
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 affine algebras and combinatorics of Young walls
Seok-Jin Kang
In this paper, we give a realization of crystal bases for quantum affine algebras using some new combinatorial objects which we call the Young walls. The Young walls consist of col…