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- W4382491188 abstract "We introduce the notions of quasi-Laurent and Laurent families of simple modules over quiver Hecke algebras of arbitrary symmetrizable types. We prove that such a family plays a similar role of a cluster in the quantum cluster algebra theory and exhibits a quantum Laurent positivity phenomenon for the basis of the quantum unipotent coordinate ring $mathcal{A}_q(mathfrak{n}(w))$, coming from the categorification. Then we show that the families of simple modules categorifying GLS-clusters are Laurent families by using the PBW-decomposition vector of a simple module $X$ and categorical interpretation of (co-)degree of $[X]$. As applications of such $mathbb{Z}$-vectors, we define several skew symmetric pairings on arbitrary pairs of simple modules, and investigate the relationships among the pairings and $Lambda$-invariants of R-matrices in the quiver Hecke algebra theory." @default.
- W4382491188 created "2023-06-29" @default.
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- W4382491188 date "2023-06-26" @default.
- W4382491188 modified "2023-09-25" @default.
- W4382491188 title "Laurent family of simple modules over quiver Hecke algebra" @default.
- W4382491188 doi "https://doi.org/10.48550/arxiv.2306.15181" @default.
- W4382491188 hasPublicationYear "2023" @default.
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