Part 2. Combinatorics of Crystal Graphs for the Root Systems of Types $A_n$, $B_n$, $C_n$, $D_n$ and $G_2$

Abstract

This note is devoted to the combinatorics of tableaux for the root systems $B_n$, $C_n$, $D_n$ and $G_2$ defined from Kashiwara's crystal graph theory. We review the definition of tableaux for types $B_n$, $C_n$, $D_n$ and $G_2$ and describe the corresponding bumping and sliding algorithms. We also derive in each case a Robinson-Schensted type correspondence.