Cluster algebras of finite type via Coxeter elements and Demazure crystals of type B,C,D

JOURNAL OF GEOMETRY AND PHYSICS

卷:137

Article

Kanakubo, Yuki¹ 

[1] Sophia Univ, Div Math, Chiyoda Ku, Kioicho 7-1, Tokyo 1028554, Japan

关键词: Cluster algebras;    Crystals;    Double Bruhat cells;    Classical groups;   

DOI  :  10.1016/j.geomphys.2018.12.001

来源: Elsevier

【 摘 要 】

For a classical group G and a Coxeter element c of the Weyl group, it is known that the coordinate ring C[G(e,c2)] of the double Bruhat cell G(e,c2) := B boolean AND B_c(2)B_ has a structure of cluster algebra of finite type, where B and B_ are opposite Borel subgroups. In this article, we consider the case G is of type B-r, C-r or D-r and describe all the cluster variables in C[G(e,c2)] as monomial realizations of certain Demazure crystals. (C) 2018 Elsevier B.V. All rights reserved.

【 授权许可】

Free