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Asymptotic Schur algebras and cellularity of q-Schur algebras

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arxiv 2305.14633 v1 pith:UX3VZVN2 submitted 2023-05-24 math.RT

Weideng Cui , Li Luo , Zheming Xu This is my paper · ORCID
classification math.RT
keywords algebrasasymptoticschurcellcellularityfiniteheckeleft
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We prove that the q-Schur algebras of finite type introduced in [LW22] are cellular in the sense of Graham and Lehrer, 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.

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  1. Geometric construction of Schur algebras

    math.RT 2024-11 conditional novelty 6.0 of 10

    For any finite type, generalized Schur algebras are realized as convolution algebras in Borel-Moore homology and equivariant K-theory of Steinberg varieties.

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