量子格拉斯曼中的素理想
Prime ideals in the quantum grassmannian
摘要：
考虑量子Grassmannian中的量子Schubert胞腔，给出了素谱通过量子Schubert胞腔的胞腔剖分.因此，我们表明，所有的素数是完全素的一般情况下，变形参数q是不是一个单位根。有一个环面H自然地作用于量子格拉斯曼，并且H素数集合的胞腔剖分通过与舒伯特细胞相关的分区上的某些图导致H谱的参数化。有趣的是，在最近关于完全非负格拉斯曼的研究中，非负细胞也发生了同样的参数化。最后，我们利用胞腔剖分证明了量子格拉斯曼方程满足正规分离性和链状性。
英文摘要：
We consider quantum Schubert cells in the quantum grassmannian and give a cell decomposition of the prime spectrum via the Schubert cells. As a consequence, we show that all primes are completely prime in the generic case where the deformation parameter q is not a root of unity. There is a torus H that acts naturally on the quantum grassmannian and the cell decomposition of the set of H-primes leads to a parameterisation of the H-spectrum via certain diagrams on partitions associated to the Schubert cells. Interestingly, the same parameterisation occurs for the non-negative cells in recent studies concerning the totally non-negative grassmannian. Finally, we use the cell decomposition to establish that the quantum grassmannian satisfies normal separation and catenarity.
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