Young tableaux and crystal $B(\infty )$ for finite simple Lie algebras

Abstract

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 $A_n$, $B_n$, $C_n$, $D_n$, and $G_2$. Connection between our realization and a previous realization of Cliff is also given.

References in corpus (5)

• Metaplectic Whittaker Functions and Crystal Bases
• Polyhedral Realizations of Crystal Bases for Quantum Algebras of Finite Types
• A combinatorial description of the Gindikin-Karpelevich formula in type A
• Young tableaux, canonical bases and the Gindikin-Karpelevich formula
• Combinatorics of the Casselman-Shalika formula in type A