On H^*(BPU_n; ℤ) and Weyl group invariants

2021/03/05 by Diarmuid Crowley, Xing Gu, Crowley, Diarmuid +1
Mathematics · #55R35 #55R40 #55T10 #Advanced Algebra and Geometry #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2103.03523

openalex publication_date 2021/03/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For the projective unitary group PU_n with a maximal torus T_PUn and Weyl group W, we show that the integral restriction homomorphism ρ_PUn \colon H^*(BPU_n;ℤ)→ H^*(BT_PUn;ℤ)^W to the integral invariants of the Weyl group action is onto. We also present several rings naturally isomorphic to H^*(BT_PUn;ℤ)^W. In addition we give general sufficient conditions for the restriction homomorphism ρ_G to be onto for a connected compact Lie group G.

Citations

• Weyl group invariants

Related

• Cohomology of BPU_n and rings of invariants of Weyl groups
• Operators on symmetric polynomials and applications in computing the cohomology of BPU_n
• Note on restriction maps of Chow rings to Weyl group invariants
• The cohomology of projective unitary groups
• Weyl group invariants