Equivariant $K$-theory of flag Bott manifolds of general Lie type

TL;DR

This paper extends the understanding of the algebraic and topological $K$-theory of flag Bott manifolds across various Lie types, generalizing previous cohomology results.

Contribution

It provides a comprehensive description of the equivariant and ordinary Grothendieck and topological $K$-rings for flag Bott manifolds of general Lie type, broadening prior cohomology findings.

Findings

Explicit descriptions of $K$-rings for flag Bott manifolds

Generalization of cohomology results to $K$-theory

Extension to all Lie types

Abstract

The aim of this paper is to describe the equivariant and ordinary Grothendieck ring and the equivariant and ordinary topological $K$-ring of flag Bott manifolds of general Lie type. This will generalize the results on the equivariant and ordinary cohomology of flag Bott manifolds of general Lie type due to Kaji Kuroki Lee and Suh.