D6(1)-geometric crystal at the spin node

Abstract

Let $\mathfrak{g}$ be an affine Lie algebra with index set $I=\{0,1,2,\dots ,n\}.$ It is conjectured that for each Dynkin node $k\in I\setminus \left\{0\right\}$ the affine Lie algebra $\mathfrak{g}$ has a positive geometric crystal. In this paper we construct a positive geometric crystal for the affine Lie algebra $D_6^{(1)}$ corresponding to the Dynkin spin node k = 6.

Communicated by Sarah Witherspoon

Keywords:

• Affine algebra
• geometric crystal

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• Primary: 17B37
• 17B67
• Secondary: 22E65
• 14M15

Additional information

Funding

KCM is partially supported by the Simons Foundation Grants nos. 307555 and 636482.