Geodesic
Extended plethystic vertex operators and plethystic universal characters
Teoretičeskaâ i matematičeskaâ fizika, Tome 214 (2023) no. 2, pp. 276-290

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By means of plethystic-type fermions and plethystic-type boson–fermion correspondence, which is a generalization of the classical boson–fermion correspondence, we obtain a two-component twisted plethystic-type symmetric functions $S_{[\lambda,\mu]}^{(\alpha,\beta)}$ from an $(\alpha,\beta)$-type boson–fermion correspondence, similarly to how the universal character $S_{[\lambda,\mu]}$ is derived from the classical boson–fermion correspondence (the twisted Jacobi–Trudi formula). As a generalization of the universal character hierarchy, we then construct the $(\alpha,\beta)$-type plethystic universal character hierarchy that contains a series of nonlinear partial differential equations of infinite order, and obtain its tau functions and Plücker relations.
Mots-clés : boson–fermion correspondence, plethystic-type fermions, Plücker relation.
Keywords: plethystic-type symmetric functions, plethystic universal character hierarchy 
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Chuanzhong Li; Yong Zhang; Huanhe Dong. Extended plethystic vertex operators and plethystic universal characters. Teoretičeskaâ i matematičeskaâ fizika, Tome 214 (2023) no. 2, pp. 276-290. http://geodesic.mathdoc.fr/item/TMF_2023_214_2_a7/