2002/11/05 by Weiqiang Wang
Mathematics · #math.QA #math.AG
published as Contemp. Math. 322 (2003), 125--140. · 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)
arxiv created 2002/11/05 · arxiv updated 2009/11/30
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.