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Adjoint Representations of Symmetric Groups

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We study the restriction to the symmetric group, \(\mathcal {S}_n\) of the adjoint representation of \(\text{GL}_n({\mathbb C})\). We determine the irreducible constituents of the space of symmetric as well as the space of skew-symmetric n × n matrices as \(\mathcal {S}_n\)-modules.

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This work was partially supported by a grant from Louisiana Board of Regents. The authors thank John Shareshian and Sheila Sundaram for useful conversations about several other proofs of our results.

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Correspondence to Mahir Bilen Can .

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Can, M.B., Jones, M. (2022). Adjoint Representations of Symmetric Groups. In: Cerejeiras, P., Reissig, M., Sabadini, I., Toft, J. (eds) Current Trends in Analysis, its Applications and Computation. Trends in Mathematics(). Birkhäuser, Cham.

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