Germán Combariza | Searcharxiv

arXiv2023

Uniqueness of factorization for fusion-invariant representations

Given a saturated fusion system $\mathcal{F}$ over a finite $p$-group $S$, we provide criteria to determine when uniqueness of factorization into irreducible $\mathcal{F}$--invariant representations holds. We use them to prove uniqueness of factorization when the order of $S$ is at most $p^3$. We also describe an example where the monoid of fusion-invariant representations is not even half-factorial. Finally, we find other examples of fusion systems where this monoid is not factorial using GAP.

math.GR↗

arXiv2019

Induced character in equivariant K-theory and wreath products

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.

math.KT↗