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arXiv · 2103.03523

On $H^*(BPU_n; \mathbb{Z})$ and Weyl group invariants

Diarmuid Crowley·Xing Gu
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Abstract

For the projective unitary group $PU_n$ with a maximal torus $T_{PU_n}$ and Weyl group $W$, we show that the integral restriction homomorphism \[\rho_{PU_n} \colon H^*(BPU_n;\mathbb{Z})\rightarrow H^*(BT_{PU_n};\mathbb{Z})^W\] to the integral invariants of the Weyl group action is onto. We also present several rings naturally isomorphic to $H^*(BT_{PU_n};\mathbb{Z})^W$. In addition we give general sufficient conditions for the restriction homomorphism $\rho_G$ to be onto for a connected compact Lie group $G$.

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Diarmuid Crowley, Xing Gu. 2021-03-05. On $H^*(BPU_n; \mathbb{Z})$ and Weyl group invariants. https://arxiv.org/abs/2103.03523

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