[图书][B] Crystal bases: representations and combinatorics

D Bump, A Schilling - 2017 - books.google.com
This unique book provides the first introduction to crystal base theory from the combinatorial
point of view. Crystal base theory was developed by Kashiwara and Lusztig from the …

Combinatorial Howe duality of symplectic type

T Heo, JH Kwon - Journal of Algebra, 2022 - Elsevier
We give a new combinatorial interpretation of Howe dual pairs of the form (g, Sp 2 ℓ), where
g is a Lie (super) algebra of classical type. This is done by establishing a symplectic …

Crystal bases of parabolic Verma modules over the quantum orthosymplectic superalgebras

IS Jang, JH Kwon, A Uruno - Journal of Algebra, 2024 - Elsevier
Crystal bases of parabolic Verma modules over the quantum orthosymplectic
superalgebras - ScienceDirect Skip to main contentSkip to article Elsevier logo Journals & …

Crystal base of the negative half of the quantum superalgebra Uq (gl (m| n))

IS Jang, JH Kwon, A Uruno - Journal of Algebra, 2023 - Elsevier
We construct a crystal base of U q (gl (m| n))−, the negative half of the quantum
superalgebra U q (gl (m| n)). We give a combinatorial description of the associated crystal B …

Super duality and crystal bases for quantum ortho-symplectic superalgebras II

JH Kwon - Journal of Algebraic Combinatorics, 2016 - Springer
Let O^ int _q (m| n) O q int (m| n) be a semisimple tensor category of modules over a
quantum ortho-symplectic superalgebra of type B, C, D introduced in Kwon (Int Math Res …

RSK correspondence and classically irreducible Kirillov–Reshetikhin crystals

JH Kwon - Journal of Combinatorial Theory, Series A, 2013 - Elsevier
We give a new combinatorial model of the Kirillov–Reshetikhin crystals of type A n (1) in
terms of non-negative integral matrices based on the classical RSK algorithm, which has a …

Lakshmibai-Seshadri paths and non-symmetric Cauchy identity

SI Choi, JH Kwon - Algebras and Representation Theory, 2018 - Springer
We give a simple crystal theoretic interpretation of the Lascoux's expansion of a non-
symmetric Cauchy kernel∏ i+ j≤ n+ 1 (1− xiyj)− 1 ∏_i+j≦n+1(1-x_iy_j)^-1, which is given …

Affine RSK correspondence and crystals of level zero extremal weight modules

JH Kwon, H Lee - Transformation Groups, 2024 - Springer
We give an affine analogue of the Robinson-Schensted-Knuth (RSK) correspondence,
which generalizes the affine Robinson-Schensted correspondence by Chmutov-Pylyavskyy …

Crystal Bases of q-deformed Kac Modules Over the Quantum Superalgebra Uq(𝔤(m|n))

JH Kwon - International Mathematics Research Notices, 2014 - ieeexplore.ieee.org
We introduce the notion of a crystal base of a finite-dimensional q-deformed Kac module
over the quantum superalgebra U_q(gl(m|n)), and prove its existence and uniqueness. In …

Rational semistandard tableaux and character formula for the Lie superalgebra ̂gl∞|∞

JH Kwon - Advances in Mathematics, 2008 - Elsevier
A new combinatorial interpretation of the Howe dual pair (glˆ∞|∞, gln) acting on an infinite-
dimensional Fock space is presented. The character of a quasi-finite irreducible highest …