Equivariant Grothendieck ring of a complete symmetric variety of minimal rank

TL;DR

This paper characterizes the G-equivariant Grothendieck ring of a regular compactification of an adjoint symmetric space of minimal rank, extending previous work on Chow rings and compactifications.

Contribution

It provides a new description of the equivariant Grothendieck ring for these varieties, generalizing prior results on Chow rings and compactifications.

Findings

Extended Brion and Joshua's results to Grothendieck rings

Described the ring structure for regular compactifications of symmetric spaces

Generalized earlier results on semisimple group compactifications

Abstract

We describe the $G$-equivariant Grothendieck ring of a regular compactification $X$ of an adjoint symmetric space $G/H$ of minimal rank. This extends the results of Brion and Joshua for the equivariant Chow ring of wonderful symmetric varieties of minimal rank and generalizes the results by the author on the regular compactification of an adjoint semisimple group.