The center of small quantum groups I: the principal block in type A
The center of small quantum groups I: the principal block in type A
复制标题
小量子群 I 的中心：A 型的主块
DOI：
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
You Qi
中科院分区：
文献类型：
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作者：
A. Lachowska;You Qi
我们发展了一个初等代数方法来计算与复半单李代数有关的小量子群在单位根处的主块的中心。对$\mathfrak{sl}_3$的例子进行了显式计算，给出了$\mathfrak{sl}_4$的进一步证据。这使得我们可以猜想：作为二重向量空间，小量子{sl}m$的单位根处的正则块的中心同构于对称群$S m}$的Haiman对角协不变代数.
We develop an elementary algebraic method to compute the center of the principal block of a small quantum group associated with a complex semisimple Lie algebra at a root of unity. The exemplary case of $\mathfrak{sl}_3$ is computed explicitly, and further evidence of $\mathfrak{sl}_4$ is sketched. This allows us to formulate the conjecture that, as a bigraded vector space, the center of a regular block of the small quantum $\mathfrak{sl}_m$ at a root of unity is isomorphic to Haiman's diagonal coinvariant algebra for the symmetric group $S_{m}$.