Abstract
We construct the polynomial induction functor, which is the right adjoint to the restriction functor from the category of polynomial representations of a general linear group to the category of representations of its Weyl group. This construction leads to a representation-theoretic proof of Littlewood’s plethystic formula for the multiplicity of an irreducible representation of the symmetric group in such a restriction. The unimodality of certain bipartite partition functions follows.
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Communicated by Gadadhar Misra.
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Narayanan, S.P., Paul, D., Prasad, A. et al. Polynomial induction and the restriction problem. Indian J Pure Appl Math 52, 643–651 (2021). https://doi.org/10.1007/s13226-021-00185-7
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DOI: https://doi.org/10.1007/s13226-021-00185-7