In this paper, we investigate a connection between convolution products for quiver Hecke algebras and tensor products for quantum groups. We give a categorification of the natural projection [Formula: see text] sending the tensor product of the highest weight vectors to the highest weight vector in terms of convolution products. When the quiver Hecke algebra is symmetric and the base field is of characteristic [Formula: see text], we obtain a positivity condition on some coefficients associated with the projection [Formula: see text] and the upper global basis, and prove several results related to the crystal bases. We then apply our results to finite type [Formula: see text] using the homogeneous simple modules [Formula: see text] indexed by one-column tableaux [Formula: see text].

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关于 quiver Hecke 代数的卷积乘积的评论

在本文中，我们研究了 quiver Hecke 代数的卷积乘积和量子群的张量乘积之间的联系。我们给出了自然投影的分类 [公式：见正文] 将最高权重向量的张量积发送到卷积积方面的最高权重向量。当 quiver Hecke 代数是对称的且基域具有特征[公式：见正文]时，我们得到与投影[公式：见正文]和上全局基相关的一些系数的正性条件，并证明了几个相关的结果到水晶基地。然后，我们使用由单列表格 [Formula: see text] 索引的同质简单模块 [Formula: see text] 将我们的结果应用于有限类型 [Formula: see text]。