Random matrices, magic squares and matching polynomials.
Random Young tableaux and combinatorial identities.
Regular character tables of symmetric groups.
Regularisation and the Mullineux map.
Representation stability for syzygies of line bundles on Segre–Veronese varieties
The rational homology groups of packing complexes are important in algebraic geometry since they control the syzygies of line bundles on projective embeddings of products of projective spaces (Segre–Veronese varieties). These complexes are a common generalization of the multidimensional chessboard complexes and of the matching complexes of complete uniform hypergraphs, whose study has been a topic of interest in combinatorial topology. We prove that the multivariate version of representation stability,...
Representations of Hecke algebras at roots of unity
Representations of the generalized symmetric groups.
Restricting supercharacters of the finite group of unipotent uppertriangular matrices.
Ribbon tableaux, Hall-Littlewood functions and unipotent varieties.
Robinson-Schensted correspondence for the signed Brauer algebras.
R-S correspondence for and Klein-4 diagram algebras.
RSK bases and Kazhdan-Lusztig cells
From the combinatorial characterizations of the right, left, and two-sided Kazhdan-Lusztig cells of the symmetric group, “ RSK bases” are constructed for certain quotients by two-sided ideals of the group ring and the Hecke algebra. Applications to invariant theory, over various base rings, of the general linear group and representation theory, both ordinary and modular, of the symmetric group are discussed.
RSK insertion for set partitions and diagram algebras.