| Macdonald I G 1995 Symmetric Functions and Hall Polynomials, 2nd edn. (Oxford: Clarendon Press) |
| Jing N H 1991 J. Algebra 138 340 |
| Sagan B E 2001 The Symmetric Group: Representations, Combinatorial Algorithms, and Symmetric Functions, 2nd edn. (New York: Springer-Verlag) |
| Date E, Kashiwara M, Jimbo M and Miwa T 1983 Transformation groups for soliton equations, in Nonlinear integrable systems-classical theory and quantum theory (Singapore: World Scientific Publishing) |
| You Y 1989 Adv. Ser. Math. Phys. 7 449 |
| Jimbo M, Miwa T and Date E 2000 Solitons: Differential Equations, Symmetries and Infinite Dimensional Algebras (Cambridge: Cambridge University Press) |
| Kac V G, Rozhkovskaya N and van de Leur J 2021 J. Math. Phys. 62 021702 |
| Kac V G and van de Leur J 2022 Publ. Res. Inst. Math. Sci. 58 1 |
| Koike K 1989 Adv. Math. 74 57 |
| Tsuda T 2004 Commun. Math. Phys. 248 501 |
| Ogawa Y 2009 Tokyo J. Math. 32 350 |
| Huang F and Wang N 2020 J. Math. Phys. 61 061508 |
| Shi L J, Wang N and Chen M R 2021 J. Nonlinear Math. Phys. 28 292 |
| Huang F and Li C Z 2024 Physica D 461 134110 |
| Fauser B, Jarvis P D and King R C 2010 J. Phys. A 43 405202 |
| Fauser B, Jarvis P D and King R C 2016 J. Phys. A 49 425201 |
| An R, Wang N and Yan Z W 2024 J. Math. Phys. 65 013505 |
| Wang N and Li C Z 2019 Glasg. Math. J. 61 601 |
| Li C Z, Zhang Y and Dong H H 2023 Theor. Math. Phys. 214 238 |
| Li D H and Yan Z W 2024 Generalized universal characters, B-type of generalized universal characters and symplectic generalized universal characters, submit to publication |
| Necoechea G and Rozhkovskaya N 2020 J. Math. Sci. 247 926 |
| Huang F and Li C Z 2023 J. Math. Phys. 64 012501 |
| Li D H, Wang F and Yan Z W 2022 Chin. Phys. B 31 080202 |
| Li D H, Jia Y J and Yan Z W 2022 Int. J. Geom. Methods Mod. Phys. 19 2250123 |
| Ikeda T 2007 Adv. Math. 215 1 |
| Ikeda T and Narsue H 2009 Trans. Amer. Math. Soc. 361 5193 |
| Olshanski G, Regev A and Vershik A 2003 Progr. Math. 210 251 |
| Ivanov V N 2005 J. Math. Sci. 131 5495 |
| Korotkikh S 2017 J. Math. Sci. 224 263 |
| Rozhkovskaya N 2019 Symmetry Integrability Geom. Methods Appl. 15 065 |
| Yang Q and Li C Z 2022 J. Math. Phys. 63 113503 |