分圆q-网范畴的分解矩阵
Decomposition matrices of cyclotomic $q$-web categories
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中文总结 AI 辅助
该研究构造了介于分圆Hecke代数与分圆q-Schur代数之间的分圆q-网自同态代数的胞腔结构，证明其模范畴的Grothendieck群同构于量子仿射$\boldsymbol{\text{gl}}_p$的可积最高权模，推广了相关经典成果。
中文摘要 AI 辅助
我们为分圆q-网的自同态代数构造了胞腔结构，这类代数构成介于分圆Hecke代数与分圆q-Schur代数之间的新量子代数族。我们证明：当q为一般值或本原单位根时，分圆q-网的模范畴的Grothendieck群同构于量子仿射代数$\boldsymbol{\text{gl}}_p$上的可积最高权模；此外，该同构将投射不可分解模的类映射到典范基。这极大推广了Lascoux-Leclerc-Thibon、Ariki及Varagnolo-Vasserot的经典工作。
英文摘要
We develop the cellular structures for the endomorphism algebras of cyclotomic $q$-webs, which form a new family of quantum algebras sitting in between cyclotomic Hecke algebras and cyclotomic $q$-Schur algebras. We show that the Grothendieck group of a module category of the cyclotomic $q$-webs for $q$ generic or a root of unity is isomorphic to an integrable highest weight module over quantum affine $\mathfrak{gl}_p$; moreover, the isomorphism maps the classes of projective indecomposable modules to the canonical basis. This substantially generalizes the classic works of Lascoux-Leclerc-Thibon, Ariki, and Varagnolo-Vasserot.
