English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

The universal enveloping algebra of any simple Lie algebra g contains afamily of commutative subalgebras, called the quantum shift of argumentsubalgebras math.RT/0606380, math.QA/0612798. We prove that generically theiraction on finite-dimensional modules is diagonalizable and their joint spectraare in bijection with the set of monodromy-free opers for the Langlands dualgroup of G on the projective line with regular singularity at one point andirregular singularity of order two at another point. We also prove amulti-point generalization of this result, describing the spectra of commutingHamiltonians in Gaudin models with irregular singulairity. In addition, we showthat the quantum shift of argument subalgebra corresponding to a regularnilpotent element of g has a cyclic vector in any irreduciblefinite-dimensional g-module. As a byproduct, we obtain the structure of aGorenstein ring on any such module. This fact may have geometric significancerelated to the intersection cohomology of Schubert varieties in the affineGrassmannian.

Opers with irregular singularity and spectra of the shift of argument subalgebra