Papers › The center of the reflection equation algebra via quantum minors
The center of the reflection equation algebra via quantum minors
David Jordan, Noah White
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We give simple formulas for the elements cₖ appearing in a quantum Cayley-Hamilton formula for the reflection equation algebra (REA) associated to the quantum group U_q(𝔤𝔩_N), answering a question of Kolb and Stokman. The cₖ's are certain canonical generators of the center of the REA, and hence of U_q(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 cₖ's to the so-called quantum power traces, and we give a new presentation for the quantum group U_q(𝔤𝔩_N), as a localization of the REA along certain principal minors.
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