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- W4320232222 abstract "We study the cocenter of the cyclotomic quiver Hecke algebra $R^Lambda_alpha$ associated to an {it arbitrary} symmetrizable Cartan matrix $A=(a_{ij})_{i,j}in I$, $Lambdain P^+$ and $alphain Q_n^+$. We introduce a notion called piecewise dominant sequence and use it to construct some explicit homogeneous elements which span the maximal degree component of the cocenter of $R^Lambda_alpha$. We show that the minimal degree components of the cocenter of $R^Lambda_alpha$ is spanned by the image of some KLR idempotent $e(nu)$, where each $nuin I^alpha$ is piecewise dominant. As an application, we show that the weight space $L(Lambda)_{Lambda-alpha}$ of the irreducible highest weight module $L(Lambda)$ over $mathfrak{g}(A)$ is nonzero (equivalently, $R^Lambda_alphaneq 0$) if and only if there exists a piecewise dominant sequence $nuin I^alpha$." @default.
- W4320232222 created "2023-02-13" @default.
- W4320232222 creator A5054789376 @default.
- W4320232222 creator A5067520942 @default.
- W4320232222 date "2022-06-13" @default.
- W4320232222 modified "2023-10-14" @default.
- W4320232222 title "Piecewise dominant sequences and the cocenter of the cyclotomic quiver Hecke algebras" @default.
- W4320232222 doi "https://doi.org/10.48550/arxiv.2206.05953" @default.
- W4320232222 hasPublicationYear "2022" @default.
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