Universal rings arising in geometry and group theory
Abstract
Various algebraic structures in geometry and group theory have appeared to be governed by certain universal rings. Examples include: the cohomology rings of Hilbert schemes of points on projective surfaces and quasi-projective surfaces; the Chen-Ruan orbifold cohomology rings of the symmetric products; the class algebras of wreath products, as well as their associated graded algebras with respect to a suitable filtration. We review these examples, and further provide a new elementary construction and explanation in the case of symmetric products. We in addition show that the Jucys-Murphy elements can be used to clarify the Macdonald's isomorphism between the FH-ring for the symmetric groups and the ring of symmetric functions.
Cite
@article{arxiv.math/0211093,
title = {Universal rings arising in geometry and group theory},
author = {Weiqiang Wang},
journal= {arXiv preprint arXiv:math/0211093},
year = {2007}
}
Comments
Latex, 16 pages, contribution to the proceedings for Conference On Hilbert Schemes, Vector Bundles And Their Interplay With Representation Theory, Columbia, Missouri. Contemp. Math. (to apear)