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Polynomial induction and the restriction problem

Author

Listed:
  • 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)

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.

Suggested Citation

  • Sridhar P. Narayanan & Digjoy Paul & Amritanshu Prasad & Shraddha Srivastava, 2021. "Polynomial induction and the restriction problem," Indian Journal of Pure and Applied Mathematics, Springer, vol. 52(3), pages 643-651, September.
    • Handle: RePEc:spr:indpam:v:52:y:2021:i:3:d:10.1007_s13226-021-00185-7
    DOI: 10.1007/s13226-021-00185-7
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