SL(2，𝑞)表示的Stiefel-Whitney类

Pub Date : 2023-02-28 DOI:10.1515/jgth-2022-0164

Neha Malik, S. Spallone

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引用次数: 2

摘要

摘要描述了有限特殊线性群G= SL (2, F q) G=\operatorname{SL}(2，\mathbb{F}_{q})的正交表示的Stiefel-Whitney类(SWCs)。从这个计算中，我们可以回答一些关于量子力学的有趣问题。例如，我们确定了正交SWCs生成的H * * (G, Z /2) H^{*}(G，\mathbb{Z}/2\mathbb{Z})的子代数，并确定了哪些是非平凡模2欧拉类。

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Stiefel–Whitney classes of representations of SL(2, 𝑞)

Abstract We describe the Stiefel–Whitney classes (SWCs) of orthogonal representations 𝜋 of the finite special linear groups G = SL ⁡ ( 2 , F q ) G=\operatorname{SL}(2,\mathbb{F}_{q}) , in terms of character values of 𝜋. From this calculation, we can answer interesting questions about SWCs of 𝜋. For instance, we determine the subalgebra of H * ⁢ ( G , Z / 2 ⁢ Z ) H^{*}(G,\mathbb{Z}/2\mathbb{Z}) generated by the SWCs of orthogonal 𝜋, and we also determine which 𝜋 have non-trivial mod 2 Euler class.

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