11 problems

Let the affine Laumon space be the moduli space whose equivariant homology carries the relevant geometric representation, and let an iterated $W$-algebra of type $A$ and an affine…

Let an iterated $W$-algebra of type $A$ act on the equivariant homology space of an affine Laumon space, and let the shifted affine Yangian be the algebra constructed in the cited…

Let the K-theoretic equivariant Euler characteristic of an affine Laumon space be the corresponding equivariant generating function, and let the elliptic Ruijsenaars–Schneider Hami…

Let $E_r$ be the elliptic Ruijsenaars–Schneider Hamiltonians and let $\mathcal{L}_{\mathbf d}$ be the finite Laumon spaces, with generating function … The eigenvalues are denoted b…

Reduced-diagonal conjecture. This multiple is equal to $1$. Thus the zero scheme of $s$ is the diagonal with its reduced scheme-theoretic multiplicity. The paper notes that this st…

Let $V(\mu)$ be the $\mathbb{C}$-linear span of the vectors $\langle\widetilde{\ul{d}}\rangle$ for $\widetilde{\ul{d}}\in D(\mu)$, equipped with the action of…

Kuznetsov's conjecture. a) The operators $a_m$, $m\in\mathbb Z$, and the operators $\fe_i,\fh_i,\ff_i$ satisfy the relations of the Lie algebra $\widehat{\mathfrak{gl}}_n$, and equ…

Let $sB$ be the geometric Eisenstein-series constructible complex on $Bun$, with stalk $sB_\eta$ at the $GL_n$-bundle indexed by a dominant weight $\eta$. Let $\CN$ be the nilpoten…

Let $\bar B:=\,'B/(\hbar=0)=\bigoplus_{\ul{d}}H^\bullet_G(\CQ_{\ul{d}})$, and let $\mathsf U:=(\BC[\fgl_n]\rtimes U(\fgl_n))\otimes\BC[\ft]$ act on it. Let $\fg_{\leq 0}$ denote th…

Let $\fQ_{\ul{d}}$ be the Laumon space, let $\ul{\\A}{}_{\mu}$ be the integral form of the shift-of-argument subalgebra, and let $\fv_{\ul{d}}$ be the corresponding module vector.…

The quantum multiplication conjecture. The isomorphism $\Psi:V_{\ul{d}}\to\fV_{\ul{d}}$ carries the operator $M_{\\D_k}$ of quantum multiplication by $c_1(D_k)$ to the operator…