Crystal Bases for Quantum Affine Algebras and Combinatorics of Young Walls

By Seok-Jin Kang. 2002

106 citations recorded by the source corpus.

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 colored blocks with various shapes that are built on a given ground‐state wall and can be viewed as generalizations of Young diagrams. The rules for building Young walls and the action of Kashiwara operators are given explicitly in terms of combinatorics of Young walls. The crystal graph of a basic representation is characterized as the set of all reduced proper Young walls. The character of a basic representation can be computed easily by counting the number of colored blocks that have been added to the ground‐state wall. 2000 Mathematical Subject Classification: 17B37, 17B65, 81R50, 82B23.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/64ddec8d7ef11459b611a2cd09e0ef20c90fd851

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In Algebra and Number Theory

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Citations in the corpus

REPRESENTATION THEORY OF SYMMETRIC GROUPS AND THEIR DOUBLE COVERS (2002, background): “This explicit combinatorics is due to Kang [17].”
Quiver Hecke superalgebras (2011, unknown): “[Kang 03] S.-J. Kang, Crystal bases for quantum affine algebras and combinatorics of Young walls, Proc.”