On the Stiefel-Whitney classes of the representations associated with Spin(15)

TL;DR

This paper computes specific Stiefel-Whitney classes for representations of Spin(15), aiding in understanding the mod 2 cohomology of the classifying space of the exceptional Lie group E_8.

Contribution

It provides explicit calculations of Stiefel-Whitney classes for key representations of Spin(15), advancing the study of cohomological properties of related Lie groups.

Findings

Determined Stiefel-Whitney classes of the second exterior and spin representations of Spin(15)

Facilitated calculations of mod 2 cohomology for E_8

Enhanced understanding of the topology of classifying spaces

Abstract

We determine the Stiefel-Whitney classes of the second exterior representation and the spin representation of Spin(15), which are useful to calculate the mod 2 cohomology of the classifying space of the exceptional Lie group E_8.