Comultiplication for shifted Yangians and quantum open Toda lattice

从量子loop超代数到超Yangian

From quantum loop superalgebras to super Yangians

本文将Drinfeld关于Yangian与量子loop代数关系的结论推广到超代数情形，建立了一般线性李超代数的量子loop超代数与超Yangian的联系，推导了对应量子loop超代数的PBW定理，并将论证拓展至扭超Yangian，引入了扭量子loop超代数作为单侧余理想。

平移扭曲 Yangian 与经典型有限 $W$-代数

Shifted twisted Yangians and finite $W$-algebras of classical type

本文通过引入抛物型表示和截断平移扭曲 Yangian，建立其 PBW 基，并证明其同构于经典型有限 $W$-代数，从而为 B、C 型偶幂零元及 D 型双 Jordan 块幂零元提供表示。

洗牌积、退化仿射Hecke代数与量子Toda格子

Shuffle Products, Degenerate Affine Hecke Algebras, and Quantum Toda Lattice

本文从代数角度重新识别GL_N的量子Toda格子与截断移位Yangian，并通过有限Miura变换和mirabolic约简方法提出新的代数构造。

Representation Theory and the Quantum Inverse Scattering Method: The Open Toda Chain and the Hyperbolic Sutherland Model

Using the representation theory of $\frak{gl}(N,\RR)$, we express the wave function of the $GL(N,\RR)$ Toda chain, which two of us recently obtained by the Quantum Inverse Scattering Method, in terms of multiple integrals. The main tool is our generalization of the Gelfand-Zetlin method to the case of infinite-dimensional representations of $\frak{gl}(N,\RR)$. The interpretation of this generalized construction in terms of the coadjoint orbits is given and the connection with the Yangian $Y(\frak{gl}(N))$ is discussed. We also give the hyperbolic Sutherland model eigenfunctions expressed in te…