Deformed Cartan matrices and generalized preprojective algebras I: Finite type
Deformed Cartan matrices and generalized preprojective algebras I: Finite type
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DOI：
10.1093/imrn/rnac054
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发表时间：
2021-09
期刊：
影响因子：
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通讯作者：
Ryo Fujita;K. Murakami
中科院分区：
文献类型：
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作者：
Ryo Fujita;K. Murakami
在Geiss-Leclerc-Schr“o}er [Invent. 209（2017）]。作为一个应用，我们计算由Hernandel-Leclerc [J. Eur. Math.Soc.18（2016）]，并提出了一个猜想，即它们的维数与相应的Kirillov-Reshetikhin模之间的归一化$R$-矩阵的极点阶一致。
We give an interpretation of the $(q,t)$-deformed Cartan matrices of finite type and their inverses in terms of bigraded modules over the generalized preprojective algebras of Langlands dual type in the sense of Gei\ss-Leclerc-Schr\"{o}er [Invent. math. 209 (2017)]. As an application, we compute the first extension groups between the generic kernels introduced by Hernandez-Leclerc [J. Eur. Math. Soc. 18 (2016)], and propose a conjecture that their dimensions coincide with the pole orders of the normalized $R$-matrices between the corresponding Kirillov-Reshetikhin modules.