Cubic hypergeometric integrals of motion in affine Gaudin models Article Swipe
Related Concepts
Affine transformation
Motion (physics)
Hypergeometric distribution
Hypergeometric function
Mathematics
Pure mathematics
Applied mathematics
Physics
Classical mechanics
Sylvain Lacroix
,
Benoît Vicedo
,
Charles A. S. Young
·
YOU?
·
· 2020
· Open Access
·
· DOI: https://doi.org/10.4310/atmp.2020.v24.n1.a5
· OA: W2797108236
YOU?
·
· 2020
· Open Access
·
· DOI: https://doi.org/10.4310/atmp.2020.v24.n1.a5
· OA: W2797108236
We construct cubic Hamiltonians for quantum Gaudin models of affine types $\hat{\mathfrak{sl}}_M$. They are given by hypergeometric integrals of a form we recently conjectured in arXiv:1804.01480. We prove that they commute amongst themselves and with the quadratic Hamiltonians. We prove that their vacuum eigenvalues, and their eigenvalues for one Bethe root, are given by certain hypergeometric functions on a space of affine opers.
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