22 pages, minor corrections; introduction revised, statements and proofs of Proposition 4.1 and Theorem 4.2 revised, comments added on Remark 4.4, typos corrected
发表信息：
Journal of Combinatorial Theory, Series A. 154 (2018), 422-443
Let $i$ be a reduced expression of the longest element in the Weyl group of type $A$, which is adapted to a Dynkin quiver with a single sink. We present a simple description of the crystal embedding of Young tableaux of arbitrary shape into $i$-Lusztig data, which also gives an algorithm for the transition matrix between Lusztig data associated to reduced expressions adapted to quivers with a single sink.
Lusztig data of Kashiwara-Nakashima tableaux in types $B$ and $C$
我们提供了一个明确的组合描述的晶体的柏原-中岛tableaux在类型$B$和$C$嵌入到$\bi$ -Lusztig数据相关的一个家庭的减少表达式$\bi$的最长的元素$w_0$。嵌入的描述是简单和基本的，只使用Schützenberger的jeu de taquin和RSK算法。经典晶体的旋量模型作为连接Kashiwara-Nakashima tableaux和Lusztig数据的中间对象起着重要的作用。
On the Combinatorics of Crystal Graphs, I. Lusztig's Involution
在本文中，我们继续发展一个新的组合模型的不可约特征标的复半单李群。这个模型，这将被称为凹室路径模型，可以被看作是一个离散的对应Littelmann路径模型。它导致了不可约特征的组合学从李型A（其中组合学是基于Young tableaux，例如）到任意类型的广泛推广。本文的主要结果是：（1）对应于不可约表示的晶图的组合描述（这个结果包括一个基于杨-巴克斯特方程的透明证明，证明了上述描述不依赖于我们模型中涉及的选择）;（2）Lusztig对合在标准基上的组合实现（这种对合将晶体表现为自对偶偏序集，对应于最长Weyl群元素对不可约表示的作用，和推广Schutzenberger的对合tableaux）;（3）任意根系的模拟，基于杨-巴克斯特方程，Schutzenberger的滑动算法，这也被称为jeu de taquin（这个算法有许多应用的表示论的李代数类型A）。
Lusztig sheaves and integrable highest weight modules in the symmetrizable case
Max Planck Institute for Mathematics（马克斯·普朗克数学研究所）；Beijing International Center for Mathematical Research, Peking University（北京大学北京国际数学研究中心）；School of Mathematical Sciences, Beijing Normal University（北京师范大学数学科学学院）
We prove a combinatorial rule for a complete decomposition, in terms of Langlands parameters, for representations of p-adic $GL_n$ that appear as parabolic induction from a large family (ladder representations). Our rule obviates the need for computation of Kazhdan-Lusztig polynomials in these cases, and settles a conjecture posed by Lapid. These results are transferrable into various type A frameworks, such as the decomposition of convolution products of homogeneous KLR-algebra modules, or tensor products of snake modules over quantum affine algebras. The method of proof applies a quantizatio…
We are interested in the McKay quiver $Γ(G)$ and skew group rings $A*G$, where $G$ is a finite subgroup of $\mathrm{GL}(V)$, where $V$ is a finite dimensional vector space over a field $K$, and $A$ is a $K-G$-algebra. These skew group rings appear in Auslander's version of the McKay correspondence. In the first part of this paper we consider complex reflection groups $G \subseteq \mathrm{GL}(V)$ and find a combinatorial method, making use of Young diagrams, to construct the McKay quivers for the groups $G(r,p,n)$. We first look at the case $G(1,1,n)$, which is isomorphic to the symmetric group…
Quantized Howe-type dualities via Koornwinder polynomials and the X=K phenomenon
Institut Camille Jordan, Lyon 1 University（里昂第一大学）；Department of Mathematics, University of Pittsburgh（匹兹堡大学）；Institut Denis Poisson, University of Tours（图尔大学）；Department of Mathematics and Statistics, State University of New York at Albany（纽约州立大学奥尔巴尼分校）
