Chern classes of certain representations of symmetric groups

Evens, Leonard; Kahn, Daniel S.

doi:10.1090/S0002-9947-1978-0511412-2

Chern classes of certain representations of symmetric groups
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by Leonard Evens and Daniel S. Kahn

Trans. Amer. Math. Soc. 245 (1978), 309-330

DOI: https://doi.org/10.1090/S0002-9947-1978-0511412-2

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Abstract:

A formula is derived for the Chern classes of the representation id $\int {\xi :P\int {H \to {U_{pn}}} }$ where P is cyclic of order P and $\xi :H \to {U_n}$ is a fintie dimensional unitary representation of the group H. The formula is applied to the problem of calculating the Chern classes of the “natural” representations ${\pi _j}:{\mathcal {S}_j} \to {U_j}$ of symmetric groups by permutation matrices.

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