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<p>We prove that the <i>q</i>-Schur algebras of arbitrary finite type, introduced by Luo and Wang (2022), are cellular in the sense of Graham and Lehrer (1996), which is a generalization of Geck’s theorem on the cellularity of Hecke algebras of finite type. Moreover, we study special modules of the associated asymptotic Schur algebras and left cell representations of Schur algebras, which generalize Lusztig’s work about special modules of asymptotic Hecke algebras and left cell representations of Weyl groups, respectively.</p>

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Asymptotic Schur algebras and cellularity of q-Schur algebras

  • 期刊论文

  • 发表日期：

    2026年3月25日

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  • Weideng Cui,
  • Li Luo,
  • Zheming Xu

摘要

We prove that the q-Schur algebras of arbitrary finite type, introduced by Luo and Wang (2022), are cellular in the sense of Graham and Lehrer (1996), which is a generalization of Geck’s theorem on the cellularity of Hecke algebras of finite type. Moreover, we study special modules of the associated asymptotic Schur algebras and left cell representations of Schur algebras, which generalize Lusztig’s work about special modules of asymptotic Hecke algebras and left cell representations of Weyl groups, respectively.