Total Stiefel Whitney classes for real representations of $\mathrm{GL}_n$ over $\mathbb{F}_q, \mathbb{R}$ and $\mathbb{C}$

Jyotirmoy Ganguly; Rohit Joshi

Total Stiefel Whitney classes for real representations of $\mathrm{GL}_n$ over $\mathbb{F}_q, \mathbb{R}$ and $\mathbb{C}$

Representation Theory 2022-08-29 v2

Authors: Jyotirmoy Ganguly , Rohit Joshi

Abstract

We compute the total Stiefel Whitney class for a real representation $\pi$ of $\mathrm{GL}_n(\mathbb{F}_q)$ , where $q$ is odd in terms of character values of $\pi$ on order $2$ diagonal elements. We also compute the total Stiefel Whitney class of real representations of $\mathrm{GL}_n(\mathbb{R})$ and $\mathrm{GL}_n(\mathbb{C})$ .

Keywords

stiefel whitney class real representations general linear group finite fields character values

Cite

@article{arxiv.2203.01280,
  title  = {Total Stiefel Whitney classes for real representations of $\mathrm{GL}_n$ over $\mathbb{F}_q, \mathbb{R}$ and $\mathbb{C}$},
  author = {Jyotirmoy Ganguly and Rohit Joshi},
  journal= {arXiv preprint arXiv:2203.01280},
  year   = {2022}
}

Total Stiefel Whitney classes for real representations of $\mathrm{GL}_n$ over $\mathbb{F}_q, \mathbb{R}$ and $\mathbb{C}$

Abstract

Keywords

Cite

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