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arXiv · 1709.09149

The center of the reflection equation algebra via quantum minors

David Jordan·Noah White
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Abstract

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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David Jordan, Noah White. 2017-09-26. The center of the reflection equation algebra via quantum minors. https://arxiv.org/abs/1709.09149

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