Annular webs and Levi subalgebras

Data

• Title: Annular webs and Levi subalgebras
• Authors: Abel Lacabanne, Daniel Tubbenhauer and Pedro Vaz
• arXiv link: https://arxiv.org/abs/2204.00947
• Published in: J. Comb. Algebra 7 (2023), no.3-4, 283–326.
• DOI: 10.4171/JCA/76

Abstract

For any Levi subalgebra of the form $\mathfrak{l}=\mathfrak{gl}{l_1}\oplus\cdots\oplus\mathfrak{gl}{l_d}\subseteq\mathfrak{gl}_{n}$ we construct a quotient of the category of annular quantum $\mathfrak{gl}_n$ webs that is equivalent to the category of finite dimensional representations of quantum $\mathfrak{l}$ generated by exterior powers of the vector representation. This can be interpreted as an annular version of skew Howe duality, gives a description of the representation category of $\mathfrak{l}$ by additive idempotent completion, and a web version of the generalized blob algebra.

Citation

@article {MR4662314,
    AUTHOR = {Lacabanne, Abel and Tubbenhauer, Daniel and Vaz, Pedro},
     TITLE = {Annular webs and {L}evi subalgebras},
   JOURNAL = {J. Comb. Algebra},
  FJOURNAL = {Journal of Combinatorial Algebra},
    VOLUME = {7},
      YEAR = {2023},
    NUMBER = {3-4},
     PAGES = {283--326},
      ISSN = {2415-6302,2415-6310},
   MRCLASS = {17B37 (18M05 18M15 20C08)},
  MRNUMBER = {4662314},
       DOI = {10.4171/jca/76},
       URL = {https://doi.org/10.4171/jca/76},
}