Operators on symmetric polynomials and applications in computing the cohomology of BPU_n

2024/10/15 by Feifei Fan, Fan, Feifei
Mathematics · #Algebraic structures and combinatorial models #Advanced Combinatorial Mathematics #Advanced Topics in Algebra

paper · pdf · doi:10.48550/arxiv.2410.11691

Abstract

This paper studies the integral cohomology ring of the classifying space BPU_n of the projective unitary group PU_n. By calculating a Serre spectral sequence, we determine the ring stucture of H^*(BPU_n;ℤ) in dimensions ≤ 11. For any odd prime p, we also determine the p-primary subgroups of Hⁱ(BPU_n;ℤ) in the range i≤ 2p+13 for i odd and i≤ 4p+8 for i even. The main technique used in the calculation is applying the theory of Young diagrams and Schur polynomials to certain linear operators on symmetric polynomials.

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