Geodesic
Symmetries of the~multicomponent $q$-KP hierarchy on a~Grassmannian
Teoretičeskaâ i matematičeskaâ fizika, Tome 213 (2022) no. 2, pp. 214-233

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Based on the study of quantum calculus, we construct a multicomponent $q$-KP hierarchy and its additional symmetries. The additional symmetries form a multifold $W_{1+\infty}$ algebra and the generating operator of the additional symmetries can be shown to have a concise form in terms of wave functions. Furthermore, the string equation and the action of additional symmetries of the multicomponent $q$-KP hierarchy on the Grassmannian are considered. After quantization, we derive the corresponding quantum torus symmetry, whose flows constitute an interesting multifold quantum torus type Lie algebra.
Keywords: multicomponent $q$-KP hierarchy, additional symmetry, Grassmannian, quantum torus Lie algebra. 
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     author = {Chuanzhong Li and Qian Chao},
     title = {Symmetries of the~multicomponent $q${-KP} hierarchy on {a~Grassmannian}},
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Chuanzhong Li; Qian Chao. Symmetries of the~multicomponent $q$-KP hierarchy on a~Grassmannian. Teoretičeskaâ i matematičeskaâ fizika, Tome 213 (2022) no. 2, pp. 214-233. http://geodesic.mathdoc.fr/item/TMF_2022_213_2_a1/