The center of the reflection equation algebra via quantum minors

David Jordan, Noah White

Research output: Contribution to journalArticlepeer-review

Abstract

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 Uq(glN), answering a question of Kolb and Stokman. The ck's are certain canonical generators of the center of the REA, and hence of Uq(glN) 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 Uq(glN), as a localization of the REA along certain principal minors.
Original languageEnglish
Pages (from-to)308-342
Number of pages35
JournalJournal of Algebra
Volume542
Early online date8 Oct 2019
DOIs
Publication statusPublished - 15 Jan 2020

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