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

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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.