Dual canonical bases and embeddings of symmetric spaces

Huanchen Bao; Jinfeng Song

paper

Dual canonical bases and embeddings of symmetric spaces

arXiv:2505.01173

Abstract

For a connected reductive group $G_{k}$ over an algebraically closed field $k$ of char $\neq = 2$ and a fixed point subgroup $K_{k}$ under an algebraic group involution, we construct a quantization and an integral model of any affine embeddings of the symmetric space $G_{k} / K_{k}$ . We show that the coordinate ring of any affine embedding of $G_{k} / K_{k}$ admits a dual canonical basis. We further construct an integral model for the canonical embedding (that is, an embedding which is complete, simple, and toroidal) of $G_{k} / K_{k}$ . When $G_{k}$ is of adjoint type, we obtain an integral model for the wonderful compactification of the symmetric space.

v2, 24 pages. We add abelianizations of affine embeddings