Algebraic structures behind Hilbert schemes and wreath products

Details Algebraic structures behind Hilbert schemes and wreath products Algebraic structures behind Hilbert schemes and wreath products

2000-11-15

arxiv.org/abs/math/0011103v3

Contemp.Math. 297 (2002) 271-295

Mathematics

Quantum Algebra

25 pages, amsLaTex, references updated, journal version

Scientific paper

In this paper we review various strikingly parallel algebraic structures behind Hilbert schemes of points on surfaces and certain finite groups called the wreath products. We explain connections among Hilbert schemes, wreath products, infinite-dimensional Lie algebras, and vertex algebras. As an application we further describe the cohomology ring structure of the Hilbert schemes. We organize this exposition around several general principles which have been supported by various works on these subjects.

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