13 problems

Let $\mathcal F$ be a fusion system on a finite $p$-group $S$, and let $\mathcal F^z$ be a set of representatives of the fully $\mathcal F$-centralised $\mathcal F$-conjugacy class…

Gepner's fusion-potential conjecture. Such a fusion potential exists in general, for every compact Lie group $G$ and level $k$.

Let $G$ be a compact group, let $K^*_G(G)$ denote the equivariant K-theory of $G$ acting on itself by conjugation, and let $R(G)$ be the representation ring of $G$. Write…

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 $\mathcal F=\mathcal F_{(1)}$ be the fusion system in the cited table, and let $\operatorname{Ind}(\mathcal F)$ denote its set of $\mathcal F$-indecomposable characters. The ch…

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 $G=SU(n)$, let $F$ be the twisting used to define the higher twisted equivariant $K$-groups, and let $J_F$ denote the corresponding higher fusion ideal. The rational computatio…

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…

Let $G$ be a finite group, let $k$ be a field of characteristic $p$, and let $M$ be a finite-dimensional representation of $G$. Write $pj(M)$ for its growth invariant. Spectral-va…

Let $\tilde{\mathcal{S}}_n$ be the extended affine symmetric group, let $\lambda \vdash n$ be an integer partition, and let ${\underline{c}}_\lambda$ be the corresponding two-sided…

Let Steinberg's basis be the basis of the representation ring under consideration, and let the index theory inner product be the inner product defined in the paper. Orthonormality…

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