Browsing Research publications by Author "Young, Charles"
Now showing items 1-7 of 7
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An Analog of the Feigin-Frenkel homomorphism for double loop algebras
Young, Charles (2021-12-15)We prove the existence of a homomorphism of vertex algebras, from the vacuum Verma module over the loop algebra of an untwisted affine algebra, whose construction is analogous to that of the Feigin-Frenkel homomorphism ... -
Cyclotomic Gaudin models with irregular singularities
Vicedo, Benoit; Young, Charles (2017-11-01)Generalizing the construction of the cyclotomic Gaudin algebra from arXiv:1409.6937, we define the universal cyclotomic Gaudin algebra. It is a cyclotomic generalization of the Gaudin models with irregular singularities ... -
(glm, gln)-dualities in gaudin models with irregular singularities
Vicedo, Benoit; Young, Charles (2018-05-03)We establish (gl M, gl N)-dualities between quantum Gaudin models with irregular singularities. Specifically, for any M,N ∈ ℤ ≥1 we consider two Gaudin models: the one associated with the Lie algebra gl M which has a double ... -
Higher current algebras, homotopy Manin triples, and a rectilinear adelic complex
Alfonsi, Luigi; Young, Charles (2023-09-30)The notion of a Manin triple of Lie algebras admits a generalization, to dg Lie algebras, in which various properties are required to hold only up to homotopy. This paper introduces two classes of examples of such homotopy ... -
Quantum loop algebras and l-root operators
Young, Charles (2015-12-01)Let g be a simple Lie algebra and q transcendental. We consider the category C_P of finite-dimensional representations of the quantum loop algebra Uq(Lg) in which the poles of all l-weights belong to specified finite sets ... -
Quartic Hamiltonians, and higher Hamiltonians at next-to-leading order, for the affine s l 2 Gaudin model
Franzini, Tommaso; Young, Charles (2023-02-21)In this work we will use a general procedure to construct higher local Hamiltonians for the affine sl2 Gaudin model. We focus on the first non-trivial example, the quartic Hamiltonians. We show by direct calculation that ... -
The solutions of $\mathfrak{gl}_{M|N}$ Bethe ansatz equation and rational pseudodifferential operators
Huang, Chenliang; Mukhin, Evgeny; Vicedo, Benoît; Young, Charles (2019-10-01)We describe a reproduction procedure which, given a solution of the $\mathfrak{gl}_{M|N}$ Gaudin Bethe ansatz equation associated to a tensor product of polynomial modules, produces a family $P$ of other solutions called ...