23 problems

Let $U(l/k)$ be the unitary supergroup, let $C_n(U(l/k))$ be its centralizer algebra, and let $T_{l/k}$ be the representation of $S_n$ under which this algebra is considered. For c…

Let $\mathcal{SG}$ be a classical supergroup, and consider the Harish–Chandra group integral and formula in the corresponding supersymmetric setting. Serganova–Zirnbauer conjecture…

Let $\widetilde{\mathcal{O}}^{\mathrm{SL}(r|s)}$ denote the relevant superalgebra, and let $Y_{\underline{i}|\underline{\hat{\mu}}}$,…

Steinberg tensor product conjecture. For $\lambda$ 4-restricted and $\mu=(\mu_1,\dots,\mu_n)$ a highest $\operatorname{GL}(n)$-weight,

Let $G=\GL_N$, let $\Gr_N=\Gr_{\GL_N}$ be its affine Grassmannian, and let $\GL_M(\bO)\ltimes U^-_{M,N}(\bF)$ be the subgroup equipped with the additive character $\chi$ described…

Equal-rank order-independence conjecture. The partition function $Z$ does not depend on the order of the NS5-branes. In particular, the resulting partition functions are related to…

Signature-independence conjecture. The partition function $Z$ does not depend on the signatures of the NS5-branes surrounding the stack of D4-branes (or D5-branes), nor on the orde…

Minimality conjecture. Up to conjugacy, a defect subgroup $D$ of $G$ is the unique minimal splitting subgroup.

Let $N>M$, let $\Gr_{\GL_N}$ be the affine Grassmannian, and let $\ul\GL(M|N)$ be the group introduced in the source as the appropriate extension governing the $c\to\infty$ limit.…

Let $G$ be a basic classical algebraic supergroup and let $H$ be a subgroup satisfying $G_0\subset H\subset G$. Put $\mathcal T=\operatorname{Rep}_k(G)$, let $Ho\mathcal T$ be its…

Let $G$ be an algebraic supergroup with reductive even part, let $\mathcal T=\operatorname{Rep}_k(G)$, and let $\mathcal C=\operatorname{Rep}(G)^\infty$. For objects…

Let $V$ be a special module in $\mathcal{T}_n^+$, meaning that $V$ is indecomposable, $\operatorname{sdim}(V)=1$, $V^*\cong V$, and $H^0(V)$ contains the trivial module. Parity-tri…

Let $I$ be the indecomposable module described in the source: it has superdimension $1$, is self-dual under both dualities, occurs as a multiplicity-one summand of…

Let $m\geq n$, let $\mathcal{T}_{m|n}^+$ be the general tensor category, and let $L(\lambda)$ be an irreducible representation with $\operatorname{sdim}(L(\lambda))>0$. Let…

Let $\overline{\mathcal{T}}_n$ be the quotient tensor category and let $\mathcal{T}_n$ be the original category. An object $I$ of $\overline{\mathcal{T}}_n$ is invertible if it is…

Let $\mathcal{T}_n^+$ be the relevant tensor category. An indecomposable module $V$ in $\mathcal{T}_n^+$ is special if $\operatorname{sdim}(V)=1$, $V^*\cong V$, and $H^0(V)$ contai…

The oriented Brauer–Clifford category is the strict monoidal supercategory $\mathcal{OBC}$ equipped with full monoidal superfunctors … for $n\in\mathbb{N}$, and let…

For the matrix Chern–Simons model with bosonic rank parameter $p$ and fermionic rank parameter $q$, let $\widehat{\mathfrak{su}}(p|q)$ denote the affine Lie superalgebra current al…

Consider a matrix supergroup Chern–Simons model with reference state $\lvert 0\rangle$ and superdeterminant construction $S$. A ground state is a state of lowest energy satisfying…

Cremmer–Julia–Scherk's conjecture. The theory could admit a geometrical interpretation in terms of the simple supergroup $OSp(1|32)$.

Let $G=GL(m|n)$, let $\lambda$ be a weight, and let $\beta_i^{\vee}$ denote the coroots occurring in Theorem advancedKempf. Assume that $i\neq m$. Minimal-bound conjecture. Theorem…

Let $A_s$ be the algebra of supersymmetric polynomials and let $A_s(p)$ be the subalgebra defined in the paper. Generation conjecture for $A_s$. The algebra $A_s$ is generated over…

Let $R_{pol}$ be the algebra of polynomial invariants, with generators $C_r$, $\sigma_i(C_{00})$, $\sigma_j(C_{11})$, $\sigma_n(C_{11})$, and $Ber(C)$ as in the preceding construct…