反射方程代数的量子中心
The center of the reflection equation algebra via quantum minors
摘要：
我们给出简单的公式元素$c_k$出现在量子凯莱-汉密尔顿公式的反射方程代数（REA）与量子群$U_q(\mathfrak{gl}_N)$，回答一个问题的Kolb和Stokman。$c_k$是REA中心的某些正则生成元，因此也是$U_q(\mathfrak{gl}_N)$本身的正则生成元;列舍季欣用图形演算描述了它们，纳扎罗夫-塔拉索夫用量子扬吉亚函数描述了它们，古列维奇、皮亚托夫和萨波诺夫用量子舒尔函数描述了它们;然而，这些元素以前没有明确的公式。作为副产品，我们证明了一个量子吉拉德-牛顿恒等式有关的$c_k$的所谓的量子功率的痕迹，我们给一个新的介绍量子群$U_q(\mathfrak{gl}_N)$，作为本地化的REA沿某些主子式。
英文摘要：
We give simple formulas for the elements $c_k$ appearing in a quantum Cayley-Hamilton formula for the reflection equation algebra (REA) associated to the quantum group $U_q(\mathfrak{gl}_N)$, answering a question of Kolb and Stokman. The $c_k$'s are certain canonical generators of the center of the REA, and hence of $U_q(\mathfrak{gl}_N)$ itself; they have been described by Reshetikhin using graphical calculus, by Nazarov-Tarasov using quantum Yangians, and by Gurevich, Pyatov and Saponov using quantum Schur functions; however no explicit formulas for these elements were previously known. As byproducts, we prove a quantum Girard-Newton identity relating the $c_k$'s to the so-called quantum power traces, and we give a new presentation for the quantum group $U_q(\mathfrak{gl}_N)$, as a localization of the REA along certain principal minors.
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