Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1896330 | Journal of Geometry and Physics | 2011 | 18 Pages |
Abstract
For a classical simple algebraic group GG, we obtain the affirmative answer for the conjecture in Nakashima (2005) [3] that there exists an isomorphism between the geometric crystal on the flag variety and the one on the maximal unipotent subgroup U−U−.
► Let GG be a simple algebraic group and UmUm be its maximal unipotent subgroup. ► We give some criteria for the existence of a unipotent crystal on UmUm. ► The unipotent crystal induces the geometric crystal YY on UmUm. ► Let VV be the geometric crystal on the flag variety of GG. ► We describe the isomorphism between VV and YY.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
Mana Igarashi, Toshiki Nakashima,