Quantum Littlewood-Richarson Coefficients and Harish-Chandra Induction for Finite General Linear Groups

9900134这个项目关注量子线性群的分支规则及其在有限群的模表示理论中的应用。 PI将研究对称群的不可约模到其子群的不可约限制。这个问题对于描述有限单群中的子群结构至关重要。 其他应用包括组合的福克空间，一个重要的对象在数学物理。 我们还研究了一些局部有限群的群代数的双边理想结构，划分的组合学，划分恒等式，对称函数，Hecke代数以及组合学中的其他主题。本计划的主要研究领域是群论和对称群的表示论。 对称群由有限集合的所有置换组成。它是数学的中心对象之一，对于物理和化学的应用极其重要。 最近的研究结果表明，一些代表性的对称群和某些限制固体对固体模型之间的强连接。

9900134This project is concerned with the branching rules for quantum linear groups and their applications to the modular representation theory of finite groups. The PI will study irreducible restrictions of irreducible modules of the symmetric group to its subgroups. This problem is crucial for describing the subgroup structure in finite simple groups. Other applications include the combinatorics of the Fock space, an object important in mathematical physics. We also study the two-sided ideal structure of group algebras of some locally finite groups, the combinatorics of partitions, partition identities, symmetric functions, Hecke algebras, and other topics in combinatorics.The main area of research in this proposal is group theory and the representation theory of symmetric groups. The symmetric group consists of all permutations of a finite set. It is one of the central objects in mathematics, and is extremely important for applications to physics and chemistry. Recent results demonstrate a strong connection between some representations of the symmetric group and certain restricted solid-on-solid models.