5 problems

Hausel's K-theoretic conjecture. The ring of invariant functions is, as an algebra over $\mathbb C[\mathrm G]^{\mathrm G}\cong K^0_{\mathrm G}(\operatorname{pt})\otimes\mathbb C$,…

Let $S_n$ be the symmetric group on $n$ letters, let $\mathcal{R}(S_n)$ denote its representation ring, and let $f_{S_n}$ be the relevant element defining the Harrison centre…

Let $S_n$ be the symmetric group on $n$ letters, let $\mathcal{R}(S_n)$ denote its representation ring of real representations, and let $U(\mathcal{R}(S_n))$ be the group of units…

Let $J(D_1|D_2)$ be the free Jordan superalgebra with $D_1+D_2\geq 1$. Let $G$ be the acting algebraic group, let ${\mathcal R}^s(G)$ be the relevant super representation ring, let…

Spectrum conjecture. For every finite group $G$, the natural map