Year: 2026
Type: preprint
Abstract: We compute the Chern classes of irreducible representations for the dihedral groups $D_{2n}$ and the generalized quaternion groups $Q_{2^n}$. Utilizing these computations, we investigate whether every even-dimensional class in the integral group cohomology of these families can be realized as a Chern class of some complex representation. It turns out that this realizability question answers in the affirmative for the generalized quaternion groups. In contrast, it turns out that the answer for dihedral groups is erratic.
Source: arXiv (Cornell University)
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223687670