圆盘多项式加法公式的交换q-模拟

一个与q盘多项式相关的非交换离散超群

A non-commutative discrete hypergroup associated with q-disk polynomials

本文的目的是给出一个与$q$ -圆盘多项式相关的非交换离散超群的例子。这些是多项式$R_{l,m}^{(\a)}$在两个非交换的变量，这是表示通过小$q$ -雅可比多项式，并出现，为值$\a=n-2$，作为带状球面函数的量子模拟的齐性空间$U(n)/U(n-1)$。这是第一次在《易经》中发现的。在文献[1]中，我们证明了这些$q$ -圆盘多项式的一个加法公式.正是这个加法公式，将允许我们以类似于[Koo 1]的方式证明线性化系数的正性，并从它构造一个遵循[Koo 4]的DJS-超群。

Diagonalization of transfer matrix of supersymmetry $u_q(\hat{sl}(m+1|n+1))$ chain with a boundary

We study the supersymmetry $U_q(\hat{sl}(M+1|N+1))$ analogue of the supersymmetric t-J model with a boundary, in the framework of the algebraic analysis method. We diagonalize the commuting transfer matrix by using the bosonization of the vertex operator associated with the quantum affine supersymmetry.

论量子亚辛豪威对偶

On the Quantum Metaplectic Howe Duality

本文在 n=1 情形下建立辛豪威对偶的量子版本，构造量子群对的交换表示，并给出辛狄拉克算子、Fischer 分解及相关投影算子的 q-类似。

Toric varieties of Loday's associahedra and noncommutative cohomological field theories

We introduce and study several new topological operads that should be regarded as nonsymmetric analogues of the operads of little 2-disks, framed little 2-disks, and Deligne-Mumford compactifications of moduli spaces of genus zero curves with marked points. These operads exhibit all the remarkable algebraic and geometric features that their classical analogues possess; in particular, it is possible to define a noncommutative analogue of the notion of cohomological field theory with similar Givental-type symmetries. This relies on rich geometry of the analogues of the Deligne-Mumford spaces, co…