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math.QA2026
Gelfand--Tsetlin bases for representations of at roots of unity
Hao Chang, Ruiying Hou, Jian Zhang
In this paper, we construct Gelfand--Tsetlin bases for representations of at roots of unity. As an application, we obtain explicit bases for certain…
math.RT2026
Irreducibility of the tensor product of Yangian \( \mathrm{Y}(\mathfrak{gl}_{m|n}) \) evaluation modules
Vyacheslav Futorny, Zheng Li, Jian Zhang
The evaluation homomorphism from the super Yangian \( \mathrm{Y}(\mathfrak{gl}_{m|n}) \) to \( \mathrm{U}(\mathfrak{gl}_{m|n}) \) induces a \( \mathrm{Y}(\mathfrak{gl}_{m|n}) \)-mo…
math.RT2026
Super-immanants and Littlewood correspondences
Naihuan Jing, Yinlong Liu, Jian Zhang
In this paper, we introduce the notion of super-immanants for supermatrices over a supercommutative algebra. Using the super Schur-Weyl duality we show that the super immanants pla…