Geodesic
Representations of $\mathfrak{sl}(2,\mathbb{C})$ in category $\mathcal O$ and master
Teoretičeskaâ i matematičeskaâ fizika, Tome 184 (2015) no. 2, pp. 212-243
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We show that the indecomposable $\mathfrak{sl}(2,\mathbb{C})$-modules in the Bernstein–Gelfand–Gelfand category $\mathcal O$ naturally arise for homogeneous integrable nonlinear evolution systems. We then develop a new approach called the $\mathcal O$ scheme to construct master symmetries for such integrable systems. This method naturally allows computing the hierarchy of time-dependent symmetries. We finally illustrate the method using both classical and new examples. We compare our approach to the known existing methods used to construct master symmetries. For new integrable equations such as a Benjamin–Ono-type equation, a new integrable Davey–Stewartson-type equation, and two different versions of $(2+1)$-dimensional generalized Volterra chains, we generate their conserved densities using their master symmetries.
Keywords: homogeneous integrable nonlinear equation, BGG category $\mathcal O$, master symmetry, conservation law, symmetry. 
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J. P. Wang. Representations of $\mathfrak{sl}(2,\mathbb{C})$ in category $\mathcal O$ and master. Teoretičeskaâ i matematičeskaâ fizika, Tome 184 (2015) no. 2, pp. 212-243. http://geodesic.mathdoc.fr/item/TMF_2015_184_2_a2/

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