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- W2734584181 abstract "Let $ninmathbb{N}$ and $K$ be any field. For any symmetric generalized Cartan matrix $A$, any $beta$ in the positive root lattice with height $n$ and any integral dominant weight $Lambda$, one can associate a quiver Hecke algebras $R_{beta}(K)$ and its cyclotomic quotient $R_{beta}^{Lambda}(K)$ over $K$. It has been conjectured that the natural map from $R_{beta}(K)$ to $R_{beta}^{Lambda}(K)$ maps the center of $R_{beta}(K)$ surjectively onto the center of $R_{beta}^{Lambda}(K)$. A similar conjecture claims that the center of the affine Hecke algebra of type $A$ maps surjectively onto the center of its cyclotomic quotient---the cyclotomic Hecke algebra $H_n^{Lambda}$ of type $G(ell,1,n)$ over $K$. In this paper, we prove these two conjectures affirmatively. As a consequence, we show that the center of $H_n^{Lambda}$ is stable under base change and it has dimension equal to the number of $ell$-partitions of $n$. Finally, as a byproduct, we also verify a conjecture of Shan, Varagnolo and Vasserot on the grading structure of the center of $R_{beta}^{Lambda}(K)$." @default.
- W2734584181 created "2017-07-21" @default.
- W2734584181 creator A5045858327 @default.
- W2734584181 date "2017-07-09" @default.
- W2734584181 modified "2023-10-16" @default.
- W2734584181 title "On the centers of cyclotomic quiver Hecke algebras" @default.
- W2734584181 hasPublicationYear "2017" @default.
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