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arxiv: 1309.6464 · v2 · pith:ZKJOOLBRnew · submitted 2013-09-25 · 🌊 nlin.SI · math.CO· math.RT

Integrable Hierarchy of the Quantum Benjamin-Ono Equation

Maxim Nazarov , Evgeny Sklyanin This is my paper
classification 🌊 nlin.SI math.COmath.RT
keywords hamiltoniansbenjamin-onoequationfunctionshierarchyquantumsymmetricarxiv
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A hierarchy of pairwise commuting Hamiltonians for the quantum periodic Benjamin-Ono equation is constructed by using the Lax matrix. The eigenvectors of these Hamiltonians are Jack symmetric functions of infinitely many variables $x_1,x_2,\ldots$. This construction provides explicit expressions for the Hamiltonians in terms of the power sum symmetric functions $p_n=x_1^n+x_2^n+\cdots$ and is based on our recent results from [Comm. Math. Phys. 324 (2013), 831-849, arXiv:1212.2781].

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