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Bethe subalgebras in Yangians and Kirillov-Reshetikhin crystals
Vasily Krylov, Inna Mashanova-Golikova, Leonid Rybnikov
Let be a simple finite-dimensional Lie algebra and its adjoint group. For each , we consider the Bethe subalgebra , a commut…
Decomposition of Frobenius pushforwards of line bundles on wonderful compactifications
Merrick Cai, Vasily Krylov
De Concini-Procesi introduced varieties known as wonderful compactifications, which are smooth projective compactifications of semisimple adjoint groups . We study the Frobenius…
Subregular nilpotent orbits and explicit character formulas for modules over affine Lie algebras
Roman Bezrukavnikov, Victor Kac, Vasily Krylov
Let be a simple finite dimensional complex Lie algebra and let be the corresponding affine Lie algebra. Kac and Wakimoto observed that in so…
Bethe subalgebras in antidominantly shifted Yangians
Vasily Krylov, Leonid Rybnikov
The loop group of a simple complex Lie group has a natural Poisson structure. We introduce a natural family of Poisson commutative subalgebras $\overline{\mathbf{…