Abstract
For a classical group G and a Coxeter element c of the Weyl group, it is known that the coordinate ring ℂ[Ge,c2] of the double Bruhat cell Ge,c2≔B∩B−c2B− 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 Br, Cr or Dr and describe all the cluster variables in ℂ[Ge,c2] as monomial realizations of certain Demazure crystals.
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