Induced character in equivariant K-theory and wreath products

Germán Combariza; Juan Rodríguez; Mario Velásquez

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arXiv · 1902.07097

Induced character in equivariant K-theory and wreath products

Germán Combariza·Juan Rodríguez·Mario Velásquez

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Abstract

Let $G$ be a finite group, $X$ be a compact $G$-space. In this note we study the $(\mathbb{Z}_ + \times\mathbb{Z}/2\mathbb{Z})$-graded algebra $$\mathcal{F}^q_G(X) = \bigoplus_{n\geq0} q^n \cdot K_{G\wr\mathfrak{S}_n}(X^n)\otimes\mathbb{C},$$ defined in terms of equivariant K-theory with respect to wreath products as a symmetric algebra. More specifically, let $H$ be another finite group and $Y$ be a compact $H$-space, we give a decomposition of $\mathcal{F}^q_{G\times H}(X\times Y)$ in terms of $\mathcal{F}^q_G(X)$ and $\mathcal{F}^q_H(Y)$. For this, we need to study the representation theory of pullbacks of groups. We discuss also some applications of the above result to equivariant connective K-homology.

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BibTeX RIS

Germán Combariza, Juan Rodríguez, Mario Velásquez. 2019-02-19. Induced character in equivariant K-theory and wreath products. https://arxiv.org/abs/1902.07097

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