RSK bases and Kazhdan-Lusztig cells

Abstract

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 Heckealgebra. Applications to invariant theory, over various base rings, of the general linear group and representation theory, both ordinary and modular, of the symmetricgroup are discussed.