## Mathematical Society of Japan Memoirs

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

Cédric Lecouvey

#### 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.

#### Chapter information

Source
Arkady Berenstein, David Kazhdan, Cédric Lecouvey, Masato Okado, Anne Schilling, Taichiro Takagi, Alexander Veselov, Combinatorial Aspect of Integrable Systems (Tokyo: The Mathematical Society of Japan, 2007), 11-41

Dates
First available in Project Euclid: 24 November 2014

https://projecteuclid.org/euclid.msjm/1416864661

Digital Object Identifier
doi:10.2969/msjmemoirs/01701C020

Mathematical Reviews number (MathSciNet)
MR2269126

Zentralblatt MATH identifier
1131.05095

Rights
Lecouvey, Cédric. Part 2. Combinatorics of Crystal Graphs for the Root Systems of Types $A_n$, $B_n$, $C_n$, $D_n$ and $G_2$. Combinatorial Aspect of Integrable Systems, 11--41, The Mathematical Society of Japan, Tokyo, Japan, 2007. doi:10.2969/msjmemoirs/01701C020. https://projecteuclid.org/euclid.msjm/1416864661