Universal rings arising in geometry and group theory

Details Universal rings arising in geometry and group theory Universal rings arising in geometry and group theory

2002-11-05

arxiv.org/abs/math/0211093v1

Contemp. Math. 322 (2003), 125--140.

Mathematics

Quantum Algebra

Latex, 16 pages, contribution to the proceedings for Conference On Hilbert Schemes, Vector Bundles And Their Interplay With Re

Scientific paper

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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