Dual canonical bases and embeddings of symmetric spaces

2025/05/02 by Huanchen Bao, Bao, Huanchen, Jinfeng Song +1 · 3 citations
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #FOS: Mathematics #Mathematics and Applications #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2505.01173

openalex publication_date 2025/05/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a connected reductive group G_k over an algebraically closed field k of char ≠ 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.

Cited by

• Reductive monoids and cluster algebras
• Symmetric subgroup schemes
• Toroidal embedding of Chevalley groups over ℤ

Related

• Coordinate rings on symmetric spaces
• Generic representations for symmetric spaces
• From groups to symmetric spaces
• The algebra of K-invariant vector fields on a symmetric space G/K
• Monoid Embeddings of Symmetric Varieties