Stokes phenomenon, Gelfand–Zeitlin systems and relative Ginzburg–Weinstein linearization
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DOI: 10.1016/j.aim.2018.09.012
Abstract: In 2007, Alekseev-Meinrenken proved that there exists a Ginzburg-Weinstein diffeomorphism from the dual Lie algebra ${\rm u}(n)^*$ to the dual Poisson Lie group $U(n)^*$ compatible with the Gelfand-Zeitlin integrable systems. In this paper, we explicitly… read more here.
Keywords: weinstein linearization; gelfand zeitlin; stokes phenomenon; ginzburg weinstein ... See more keywords
Canonical Gelfand–Zeitlin Modules over Orthogonal Gelfand–Zeitlin Algebras
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DOI: 10.1093/imrn/rnz002
Abstract: We prove that every orthogonal Gelfand–Zeitlin algebra $U$ acts (faithfully) on its Gelfand–Zeitlin subalgebra $\Gamma $. Considering the dual module, we show that every Gelfand–Zeitlin character of $\Gamma $ is realizable in a $U$-module. We… read more here.
Keywords: gelfand zeitlin; orthogonal gelfand; zeitlin modules; zeitlin ... See more keywords