Photo by vika_strawberrika from unsplash
ABSTRACT Let G be a simply connected simple algebraic group over ℂ of type Br, B and B− be its two opposite Borel subgroups, and W be the associated Weyl… Click to show full abstract
ABSTRACT Let G be a simply connected simple algebraic group over ℂ of type Br, B and B− be its two opposite Borel subgroups, and W be the associated Weyl group. For u, v∈W, it is known that the coordinate ring ℂ[Gu,v] of the double Bruhat cell is isomorphic to an upper cluster algebra and generalized minors Δ(k;i) are the cluster variables of ℂ[Gu,v][1]. It is also shown that ℂ[Gu,v] have a structure of cluster algebra [6]. In the case v = e, we shall describe the generalized minor Δ(k;i) explicitly.
Keywords:
explicit forms;
forms cluster;
double bruhat;
cluster variables;
variables double;
bruhat cells
Journal Title: Communications in Algebra
Year Published: 2017
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!
Journal Title: Communications in Algebra
Year Published: 2017
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!