15 problems

Let $G$ be a reductive algebraic group with Weyl group $W$, let $p$ denote the characteristic of the ground field, and let Springer representations mean the representations of $W$…

Let $R_0$ be a root system of type $B_n$, let $\bbH$ be the associated graded Hecke algebra with long-root label $k_1\neq 0$ and short-root label $k_2=mk_1$, where…

Lusztig's special-representation conjecture. All special representations should be assigned, via Springer correspondence, to nilpotent orbits with the trivial local system, so that…

Springer-correspondence conjecture. The module $L_\chi$ corresponds to $\mathbb O_\chi^{(1)}$ via the Springer correspondence, and $\mathsf{sign}\otimes L_\chi$ corresponds to…

Let $G$ be a connected complex reductive group with Weyl group $W$, let $\psi\in\operatorname{Irr}(W)$ be inflated from a quotient … and let $\alpha_{\psi,G}^{z}$ be the Laurent po…

Stable wavefront-set conjecture. One has

Let ${\mathfrak g}$ be a complex semisimple Lie algebra, let $G=\operatorname{Aut}({\mathfrak g})^0$, and let ${\mathcal B}$ be its flag variety. Fix a Borel subalgebra…

Let rigid semisimple operators be labeled by pairs of partitions $(\lambda^{'},\lambda^{”})$. Fix a fingerprint invariant, and consider operators satisfying different conditions in…

A rigid semisimple operator is labeled by a pair of partitions $(\lambda^{'},\lambda^{”})$. The symbol invariant describes the Springer correspondence for classical groups, while t…

Transpose-partition conjecture. One should be able to construct a gGGr in which $\rho$ is realized with multiplicity one from an element of the nilpotent orbit whose associated par…

Fourier-transform Springer correspondence. If $\lambda$ has at least one odd part, then $\mathfrak F$ induces a bijection

Let $\mathbb{O}$ be a special nilpotent orbit, let $\lambda$ be a dominant representative of a regular central character, and let $W_\lambda$ be its integral Weyl group. For…

Let $G$ be the reductive group with Lie algebra $\frak{g}$, let $F$ be the relevant local field, and let $\tilde{W}=\tilde{W}$ be the extended affine Weyl group. For a regular semi…

Assume that $G$ is almost simple and simply connected, and that condition 0.1(i) holds. Let $f700$ be a $C$-small conjugacy class in $G$, and let $f701$ and $u$ be commuting semisi…

Let $G=SL_2$ (and, in the proposed extension, consider the type-$A_n$ setting), let ${\mathfrak g}$ be the Lie algebra with nilpotent cone ${\mathcal N}$, and let…