Equivariant K-theory, wreath products and Heisenberg algebra
Equivariant K-theory, wreath products and Heisenberg algebra
复制标题
等变 K 理论、花圈积和海森堡代数
DOI：
--
复制
发表时间：
1999
期刊：
影响因子：
--
通讯作者：
Weiqiang Wang
中科院分区：
文献类型：
--
作者：
Weiqiang Wang
给定有限群 G 和 G 空间 X，我们证明直和 $F_G (X) = igoplus_{n geq 0}K_{G_n} (X^n) igotimes C$ 承认自然分级 Hopf 代数和 $lambda$ 环结构，其中 $G_n$ 表示花环积 $G sim S_n$。作为分级代数，$F_G (X)$ 在 $K_G(X) igotimes C$ 方面与某个超对称乘积同构。我们进一步证明 $F_G (X)$ 与无限维海森堡（超）代数的 Fock 空间同构。作为几个应用程序之一，我们计算轨道欧拉特征 $e(X^n, G_n)$。
Given a finite group G and a G-space X, we show that a direct sum $F_G (X) = igoplus_{n geq 0}K_{G_n} (X^n) igotimes C$ 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 $K_G(X)igotimes C$ 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 $e(X^n, G_n)$.