Eigenvalues of Bethe vectors in the Gaudin model

Molev, A.I.; Mukhin, E.E.

doi:10.1134/S0040577917090021

Eigenvalues of Bethe vectors in the Gaudin model

Oct 1, 2017

24 pages

Published in:

Theor.Math.Phys. 192 (2017) 3, 1258-1281

Published: Oct 1, 2017

DOI:

10.1134/S0040577917090021

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Abstract: (Springer)

According to the Feigin–Frenkel–Reshetikhin theorem, the eigenvalues of higher Gaudin Hamiltonians on Bethe vectors can be found using the center of an affine vertex algebra at the critical level. We recently calculated explicit Harish-Chandra images of the generators of the center in all classical types. Combining these results leads to explicit formulas for the eigenvalues of higher Gaudin Hamiltonians on Bethe vectors. The Harish-Chandra images can be interpreted as elements of classical W-algebras. By calculating classical limits of the corresponding screening operators, we elucidate a direct connection between the rings of q-characters and classical W-algebras.

Gaudin Hamiltonian
Bethe vector
q-character
classical W-algebra

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Figures(0)

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