48 problems

Let $G=\mathrm{GL}_{d}$, and let affine Springer fibers be defined by elements whose root valuation datum is specified. Goresky–Kottwitz–MacPherson conjecture. The cohomology of th…

Let … where $z_i\in\mathbb{C}^*$ are pairwise distinct and $d_i\geq0$. Equivariant formality conjecture. The affine Springer fiber $\mathrm{Sp}_{\gamma}$ is equivariantly formal fo…

Let $\mathcal{P}$ be the Procesi bundle on $\operatorname{Hilb}^n(\mathbb{C}^2)$, let $\mathcal{P}^*$ denote its dual, and let $\mathcal{O}(d)$ be the indicated determinant-line-bu…

A generalized affine Springer fiber is the variety associated with a reductive group, a finite-dimensional representation, and an element of the corresponding loop-space representa…

Let $k$ be an algebraically closed field with $\mathop{\rm char}(k) \not= 2$, and let the maximal torus split as $E^{\times} \times F^{\times}$, where $E/F$ is a quadratic extensio…

Let $u$ be the parameter in the computed family of non-admissible $W$-algebras, and let the cohomology groups be those arising from the fixed varieties described in the paper. Coho…

Let $W$ be a $C_2$-cofinite non-admissible $W$-algebra, and let the associated generalized affine Springer fiber construction assign fixed loci, affine Weyl-group labels, simple mo…

Let $G$ be a simply-connected reductive group, let $\\g\in\mathfrak{g}((t))$ be topologically nilpotent, and let $A_{\g}$ denote the component-group action on the affine Springer f…

Let $\mathcal{M}_\psi$ be the moduli space equipped with its Dolbeault complex structure and given holomorphic symplectic form, let $\mathbb{X}_*(T)$ be the cocharacter lattice act…

Let $B^{\vee,+}$ and $B^{\vee,-}$ be opposite Borel subgroups of $G^{\vee}$ with $B^{\vee,+}\cap B^{\vee,-}=T^{\vee}$. Set $\mathcal{W}=B^{\vee,-}B^{\vee,+}\subset G^{\vee}$, let…

Let $G$ be the reductive group underlying the affine Grassmannian, let $L^{\heartsuit}{\mathfrak g}$ be the space of elements under consideration, and for…

The small quantum group and the semi-infinite flag variety are related to affine Springer fibers through the proposed geometric and categorical constructions described in the paper…

Let $0\leq d_1\leq\cdots\leq d_1$, let $\beta=\operatorname{JM}_n^{d_1}\ldots\operatorname{JM}_2^{d_{n-1}}$, and set $J=J(d_1,\ldots,d_n)$, where … The notation…

Let $\mathbb{G}$ be a quasi-split generic group, and let the local systems, perverse filtrations, rational DAHA actions, and braid-group actions be defined as in the split case. Ob…

Let $G$ be a reductive group, let $\mathcal A_G=\bigoplus_{d=0}^{\infty}{}_0\mathcal A_d$ be the graded Coulomb branch algebra, and for $\gamma\in\mathfrak g$ define … Let…

Let $\gamma$ be an unramified element with associated link $L_{\gamma}$, let $\mathrm{Sp}_{\gamma}$ be its affine Springer fiber, and let $\mathrm{gr}_P$ be the specified perverse…

Let $gamma in \mathfrak{gl}_n((t))$ have reduced spectral curve, let $\mathrm{Sp}_{\gamma}$ be its affine Springer fiber, and let $L_{\gamma}$ be the link of the spectral curve sin…

Let $P\subset G$ be a parabolic subgroup, let $\widetilde{N}=T^*(G/P)$ be the corresponding Springer resolution, and let $T\widetilde{N}$ be its tangent bundle. The dilation action…

Let $\Fl^{\gamma,+}_{\bI}$ be the positive part of the affine Springer fiber, let $\Lambda^+$ be its positive lattice action, and let $\chi_\lambda$ denote a nontrivial irreducible…

Let $G=GL_n$, let $\gamma$ be the regular element used to define the affine Springer fiber $\Fl^{\gamma}_{\bI}$, let $\Lambda$ be the lattice acting on it, and let $P$ be the perve…

BBASV's conjecture. The embedding above is an isomorphism.

Center–cohomology isomorphism conjecture. The algebra embedding

Let $G$ be quasisimple of adjoint type, let $cmathfrak g=\operatorname{Lie}(G)$, and let $\operatorname{cox}\bin W$ be a Coxeter element of order $n$. For $m$ coprime to $n$, let…

Let $cmathfrak g=\operatorname{Lie}(GL_n)$ or $cmathfrak g=\operatorname{Lie}(SL_n)$, and let $gammabin g(cO)$ be elliptic, regular semisimple, and topologically nilpotent. Let…

Let $G=PGL_n$, let $cmathfrak g=\operatorname{Lie}(PGL_n)$, and let $gammabin g(cO)$ be elliptic, regular semisimple, and topologically nilpotent. Let $[operatorname{Sp}gamma]$ den…