Abstract
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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M.B. Can, A representation on the labeled rooted forests. Commun. Algebra 46(10), 4273–4291 (2018)
M.B. Can, J. Remmel, Loop-augmented forests and a variant of Foulkes’s conjecture. Algebr. Comb. 1(5), 573–601 (2018)
M.B. Can, Y. Cherniavsky, T. Twelbeck, Bruhat order on partial fixed point free involutions. Electron. J. Combin. 21(4) (2014). Paper 4.34
N.A. Loehr, J. Remmel, A computational and combinatorial exposé of plethystic calculus. J. Algebr. Combin. 33(2), 163–198 (2011)
Acknowledgements
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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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. https://doi.org/10.1007/978-3-030-87502-2_47
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DOI: https://doi.org/10.1007/978-3-030-87502-2_47
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