$U_ε^{res}(sl_2)$在限制q-Fock空间上的表示

"Spread" restricted Young diagrams from a 2D WZNW dynamical quantum group

The Fock representation of the Q-operator algebra for the diagonal WZNW model on SU(n) at level k, where Q is the matrix of the 2D WZNW "zero modes" generating certain dynamical quantum group, is finite dimensional and has a natural basis labeled by su(n) Young diagrams Y of "spread" not exceeding h := k+n (spr (Y) = #(columns) + #(rows))

推广手征su（2）WZNW模型的零模融合环和辫群表示

Zero modes' fusion ring and braid group representations for the extended chiral su(2) WZNW model

扩展的手征$su(2)$ WZNW模型的零模Fock空间为在偶数（$2h$ -th）单位根上实现受限$U_q sl(2)$量子通用包络代数（QUEA）的表示的Grothendieck融合环及其通过Lusztig算子的扩展提供了空间。它示出，表示的Drinfeld图像的规范字符的Casimir不变量$C$的Chebyshev多项式允许一个流线型的推导$C$的特征方程从限定的QUEA的定义关系。零模Fock空间中QUEA的Lusztig推广的融合环的性质与推广的$su(2)_{h-2}$电流代数模型的原场关联函数的编织性质有关.

高阶q-变形Fock空间的典范基

Canonical bases of higher-level q-deformed Fock spaces

定义了仿射李代数sl（n）^的高阶q-变形Fock空间模的标准基.这推广了Leclerc和Thibon对于水平1的情况的结果。我们用仿射Kazhdan-Lusztig多项式表示Fock空间的标准基和自然基之间的转移阵。

SL_2中曲面群表示的量子迹

Quantum traces for representations of surface groups in SL_2

我们考虑由SL_2中曲面群的所有表示组成的特征标簇的两种不同的量子化。一个是由Przytycki-Sikora和Turaev考虑的绞代数。另一个是由Chekhov-Fock和Kashaev引入的量子Teichmuller空间。我们构造了一个同态从绞代数的量子Teichmuller空间，当限制的经典情况下，对应于这两个代数之间的等价通过迹函数。

Representations for three-point Lie algebras of genus zero

In this paper, we study representations for three-point Lie algebras of genus zero based on the Cox-Jurisich's presentations. We construct two functors which transform simple restricted modules with nonzero levels over the standard affine algebras into simple modules over the three-point affine algebras of genus zero. As a corollary, vertex representations are constructed for the three-point affine algebra of genus zero using vertex operators. Moreover, we construct a Fock module for certain quotient of three-point Virasoro algebra of genus zero.

Higher level Fock spaces and affine Yangian

We construct actions of the affine Yangian of type A on higher level Fock spaces by extending known actions of the Yangian of finite type A due to Uglov. This is a degenerate analog of a result by Takemura-Uglov, which constructed actions of the quantum toroidal algebra on higher level $q$-deformed Fock spaces.