Supersymmetric rigged configurations and crystals of quantum affine supergroups

除了2篇关于组合表示论的论文被发表外，另外4篇论文出现在arXiv预印本服务器上，如下所示。我写了一篇关于划分代数的细胞子代数的论文。我们描述了各种图代数和他们的表示理论使用细胞代数的格雷厄姆和莱勒和分解成半图。我们给出了一个新的构造，从一般的细胞代数和我们称之为细胞圈积的rook Brauer代数的子代数中构建新的细胞代数。我与人合著了一篇关于Hayashi在1990年引入的量子Clifford代数的广义定义的论文，使用了另一个参数k，我们称之为扭曲，这对我的合著者后来关于量子偏斜豪对偶的工作至关重要，并与Faddeev，Reshetikhin，和Takhtajan。第二篇关于晶体结构的合理提升以研究不变量环的论文已经完成，建立在我们去年的第一篇论文的基础上。最后，第一个系列的至少3个文件之间的联系舒伯特微积分和随机粒子过程完成并上传。

In addition to 2 papers on combinatorial representation theory being published, an additional 4 papers appeared on the arXiv preprint server, as follows.I authored a paper on cellular subalgebras of the partition algebra. We described various diagram algebras and their representation theory using cellular algebras of Graham and Lehrer and the decomposition into half diagrams. We gave a new construction to build new cellular algebras from a general cellular algebra and subalgebras of the rook Brauer algebra that we call the cellular wreath product.I coauthored a paper on a generalized definition for the quantum Clifford algebra introduced by Hayashi in 1990 using another parameter k that we call the twist, which was essential for my coauthor's subsequent work on quantum skew Howe duality and made a new connection with the alternative construction of Faddeev, Reshetikhin, and Takhtajan.The second paper on rational lifting of crystal structures to study the ring of invariants was completed, building on our first paper from last year.Lastly, the first of a series of at least 3 papers on the connection between Schubert calculus and stochastic particle processes was finished and uploaded.