Supersymmetric rigged configurations and crystals of quantum affine supergroups

除了已发表的2篇关于组合表示理论的论文外，arxiv预印本服务器上还出现了另外4篇论文，具体如下：我撰写了一篇关于划分代数的细胞子代数的论文。我们用Graham和Lehrer的元胞代数刻画了各种图代数及其表示理论，并将其分解成半图。我们给出了一种新的构造，从一个一般的胞代数和rook Brauer代数的子代数中构造出新的胞代数，我们称之为胞环积。我与人合著了一篇关于量子Clifford代数的广义定义的论文，该定义由Hayashi在1990年引入，使用另一个我们称为twist的参数k，这是我的合著者随后关于量子斜Howe对偶的重要工作，并与Faddeev，Reshetikhin和Takhtajan的另一种构造建立了新的联系。第二篇关于晶体结构的有理提升来研究不变量环的论文，是在我们去年的第一篇论文的基础上完成的。最后，关于舒伯特微积分和随机粒子过程之间的联系的至少3篇系列论文中的第一篇已经完成并上传。

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.