Adams operations on classical compact Lie groups

TL;DR

This paper provides explicit formulas for Adams operations on the K-theory of classical compact Lie groups, including eigenvectors for the unitary group, enhancing understanding of their algebraic structure.

Contribution

It introduces new explicit formulas for Adams operations on K-theory of classical Lie groups and identifies eigenvectors for $U(n)$, advancing computational methods in algebraic topology.

Findings

Explicit formulas for Adams operations on $K^*(G)$ for classical groups

Eigenvectors of Adams operations on $K^*(U(n))$ identified

Enhanced computational tools for algebraic topology

Abstract

Let $G$ be $U(n)$, $SU(n)$, $Sp(n)$ or $Spin(n)$. In this short note we give explicit general formulas for Adams operations on $K^*(G)$, and eigenvectors of Adams operations on $K^*(U(n))$.