Equivariant K-theory, wreath products, and Heisenberg algebra

Details Equivariant K-theory, wreath products, and Heisenberg algebra Equivariant K-theory, wreath products, and Heisenberg algebra

1999-07-23

arxiv.org/abs/math/9907151v2

Duke Math. J. 103 (2000) 1--23

Mathematics

Quantum Algebra

23 pages, some reorganizations and improvement of presentations, and other minor changes, to appear in Duke Math. J

Scientific paper

Given a finite group G and a G-space X, we show that a direct sum $F_G (X) = \bigoplus_{n \geq 0}K_{G_n} (X^n) \bigotimes \C$ admits a natural graded Hopf algebra and $\lambda$-ring structure, where $G_n$ denotes the wreath product $G \sim S_n$. $F_G (X)$ is shown to be isomorphic to a certain supersymmetric product in terms of $K_G(X)\bigotimes \C$ as a graded algebra. We further prove that $F_G (X)$ is isomorphic to the Fock space of an infinite dimensional Heisenberg (super)algebra. As one of several applications, we compute the orbifold Euler characteristic $e(X^n, G_n)$.

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