Crystal Graphs and Young Tableaux

Crystal Bases and Young Tableaux

Young Tableaux and Crystal B(∞) for Finite Simple Lie Algebras

We study the crystal base of the negative part of a quantum group. An explicit realization of the crystal is given in terms of Young tableaux for types An, Bn, Cn, Dn, and G2. Connection between our realization and a previous realization of Cliff is also given.

Involutions on Standard Young Tableaux and Divisors on Metric Graphs

We elaborate upon a bijection discovered by Cools, Draisma, Payne, and Robeva in [CDPR12] between the set of rectangular standard Young tableaux and the set of equivalence classes of chip configurations on certain metric graphs under the relation of linear equivalence. We present an explicit formula for computing the v0-reduced divisors (representatives of the equivalence classes) associated to...

Young tableaux

This paper gives a qualitative description how Young tableaux can be used to perform a Clebsch-Gordan decomposition of tensor products in SU(3) and how this can be generalized to SU(N).

Correspondence between Young Walls and Young Tableaux Realizations of Crystal Bases for the Classical Lie Algebras

We give a 1-1 correspondence with the Young wall realization and the Young tableau realization of the crystal bases for the classical Lie algebras. Introduction Young tableaux and Young walls play important roles in the interplay, which can be explained in a beautiful manner using the crystal base theory for quantum groups, between the fields of representation theory and combinatorics. Indeed, ...