On the spectral problem of the quantum KdV hierarchy

被引:1
|
作者
Ruzza, Giulio [1 ]
Yang, Di [2 ]
机构
[1] UCLouvain, IRMP, B-1348 Louvain La Neuve, Belgium
[2] USTC, Sch Math Sci, Hefei 230026, Peoples R China
关键词
deformed Schur polynomials; double ramification hierarchy; quantum integrable system; spectral problem; Young-Jucys-Murphy elements; CONFORMAL FIELD-THEORY; DOUBLE RAMIFICATION CYCLES; INTEGRABLE STRUCTURE; OPERATOR;
D O I
10.1088/1751-8121/ac190a
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
The spectral problem for the quantum dispersionless Korteweg-de Vries (KdV) hierarchy, aka the quantum Hopf hierarchy, is solved by Dubrovin. In this article, following Dubrovin, we study Buryak-Rossi's quantum KdV hierarchy. In particular, we prove a symmetry property and a non-degeneracy property for the quantum KdV Hamiltonians. On the basis of this we construct a complete set of common eigenvectors. The analysis underlying this spectral problem implies certain vanishing identities for combinations of characters of the symmetric group. We also comment on the geometry of the spectral curves of the quantum KdV hierarchy and we give a representation of the quantum dispersionless KdV Hamiltonians in terms of multiplication operators in the class algebra of the symmetric group.
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页数:27
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