Corrigendum to "On the equivariant $K$-theory of the nilpotent cone in the general linear group," published in Represent. Theory 8 (2004)

TL;DR

This paper corrects and completes a previous algorithm for computing the Lusztig-Vogan bijection in the context of equivariant K-theory of the nilpotent cone for GL(n,C), ensuring its accuracy in all cases.

Contribution

It provides a necessary correction to an existing combinatorial algorithm, addressing an overlooked case to improve its completeness.

Findings

Corrected the algorithm to include an easy case previously omitted

Ensured the algorithm's applicability to all relevant cases in the theory

Enhanced the reliability of computations in equivariant K-theory for GL(n,C)

Abstract

In the paper [P. Achar, "On the equivariant $K$-theory of the nilpotent cone in the general linear group," Represent. Theory 8 (2004), 180-211], the author gave a combinatorial algorithm for computing the Lusztig-Vogan bijection for $GL(n,\mathbb{C})$. However, that paper failed to mention one easy case that may sometimes arise, making the description of the algorithm incomplete. This note fills in that gap.