Polynomial induction and the restriction problem

Sridhar P. Narayanan (), Digjoy Paul, Amritanshu Prasad () and Shraddha Srivastava
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Sridhar P. Narayanan: Uppsala University
Digjoy Paul: Indian Institute of Technology Bombay
Amritanshu Prasad: The Institute of Mathematical Sciences (HBNI)
Shraddha Srivastava: Tata Institute of Fundamental Research

Indian Journal of Pure and Applied Mathematics, 2021, vol. 52, issue 3, 643-651

Abstract: 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.

Keywords: Plethysm; Restriction problem; Polynomial induction; Frobenius reciprocity; Multipartite partitions; 05E10; 05E05; 20C30 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s13226-021-00185-7

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