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Universal rings arising in geometry and group theory | | Weiqiang Wang
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5 Nov 2002 | | Journal: | Contemp. Math. 322 (2003), 125--140. | | Subject: | Quantum Algebra; Algebraic Geometry | math.QA math.AG | | 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. | | Source: | arXiv, math.QA/0211093 | | Services: | Forum | Review | PDF | Favorites | |
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