Characteristic Classes Of Representations Of Lie Groups
Representation Theory
2026-02-03 v1 Differential Geometry
Abstract
An irreducible representation of a reductive Lie algebra, when restricted to a Cartan subalgebra, decomposes into weights with multiplicity. The first part of this paper outlines a procedure to compute symmetric polynomials (e.g., power sums) of this multiset of weights, as functions of the highest weight. Next, let G be a connected reductive complex algebraic group with maximal torus T. We express the restrictions of the Chern classes of irreducible representations of G to T, as polynomial functions in the highest weight. We do the same for Stiefel-Whitney classes of orthogonal representations.
Cite
@article{arxiv.2602.02145,
title = {Characteristic Classes Of Representations Of Lie Groups},
author = {Rohit Joshi and Steven Spallone},
journal= {arXiv preprint arXiv:2602.02145},
year = {2026}
}