Cohomology of BPU_n and rings of invariants of Weyl groups

2024/07/23 by Fan, Feifei, Jiaxi Zha, Zha, Jiaxi +3
Physics and Astronomy · Mathematics · #Black Holes and Theoretical Physics #Homotopy and Cohomology in Algebraic Topology #Algebraic Geometry and Number Theory

paper · pdf · doi:10.48550/arxiv.2407.16297

Abstract

Let PU_n denote the projective unitary group of rank n and BPU_n be its classifying space, for n>1. Using the Serre spectral sequence associated to the fibration BU_n→ BPU_n→ K(ℤ,3), we compute the integral cohomology group of BPU_n in dimensions ≤ 14. In addition, we determine the ring structure of H^*(BPU_n;ℤ) up to dimension 13 by computing the ring of invariants H^*(BT_PUn)^W of the Weyl group action in dimensions ≤ 12.

Related

• Operators on symmetric polynomials and applications in computing the cohomology of BPU_n
• The cohomology of the classifying space of PU(4)
• On H^*(BPU_n; ℤ) and Weyl group invariants
• The p-primary subgroups of the cohomology of BPU_n in dimensions less than 2p+5
• The cohomology of projective unitary groups