Schur-Weyl duality, Verma modules, and row quotients of Ariki-Koike algebras

Data

• Title: Schur-Weyl duality, Verma modules, and row quotients of Ariki-Koike algebras
• Authors: Abel Lacabanne and Pedro Vaz
• arXiv link: https://arxiv.org/abs/2004.01065
• Published in: Pacific J. Math 311 (2021), No. 1, 113–133
• DOI: 10.2140/pjm.2021.311.113

Abstract

We prove a Schur-Weyl duality between the quantum enveloping algebra of $\mathfrak{gl}_m$ and certain quotient algebras of Ariki-Koike algebras, which we give explicitly. The duality involves several algebraically independent parameters and is realized through the tensor product of a parabolic universal Verma module and a tensor power of the natural representation of $\mathfrak{gl}_m$. We also give a new presentation by generators and relations of the generalized blob algebras of Martin and Woodcock as well as an interpretation in terms of Schur-Weyl duality by showing they occur as a particular case of our algebras.

Citation

@article {MR4241799,
    AUTHOR = {Lacabanne, Abel and Vaz, Pedro},
     TITLE = {Schur-{W}eyl duality, {V}erma modules, and row quotients of
              {A}riki-{K}oike algebras},
   JOURNAL = {Pacific J. Math.},
  FJOURNAL = {Pacific Journal of Mathematics},
    VOLUME = {311},
      YEAR = {2021},
    NUMBER = {1},
     PAGES = {113--133},
      ISSN = {0030-8730,1945-5844},
   MRCLASS = {20C08 (20G42)},
  MRNUMBER = {4241799},
       DOI = {10.2140/pjm.2021.311.113},
       URL = {https://doi.org/10.2140/pjm.2021.311.113},
}