arXiv math/02110932002-11-05math.QAmath.AG

Universal rings arising in geometry and group theory

Weiqiang Wang

备注：: 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)
发表信息：: Contemp. Math. 322 (2003), 125--140.

英文摘要：

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.

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