Related papers: Capped Vertex Functions for $\text{Hilb}^n (\mathb…

We generalize the construction of elliptic stable envelopes to actions of connected reductive groups and give a direct inductive proof of their existence and uniqueness in a rather general situation. We show these have powerful enumerative…

We describe the graded characters and Hilbert functions of certain graded artinian Gorenstein quotients of the polynomial ring which are also representations of the symmetric group. Specifically, we look at those algebras whose socles are…

We study the closed convex hull of various collections of Hilbert functions. Working over a standard graded polynomial ring with modules that are generated in degree zero, we describe the supporting hyperplanes and extreme rays for the…

Using vertex operator we study Macdonald symmetric functions of rectangular shapes and their connection with the q-Dyson Laurent polynomial. We find a vertex operator realization of Macdonald functions and thus give a generalized Frobenius…

We continue the study of automorphic functions associated with a curve $C$ over the ring $k[\epsilon]/(\epsilon^2)$, where $k$ is a finite field, begun in arXiv:2303.16259. Namely, we study an example of theta-lifting in this framework and…

We outline a cohomological treatment for multivalued (classical) action functionals. We point out that an application of Takens' theorem, after Zuckerman, Deligne and Freed, allows to conclude that multivalued functionals yield globally…

In this paper we compute the Hilbert functions of irreducible (or smooth) and reduced arithmetically Gorenstein schemes that are twisted anti-canonical divisors on arithmetically Cohen-Macaulay schemes. We also prove some folklore results…

The n-point correlation functions introduced by Bloch and Okounkov have already found several geometric connections and algebraic generalizations. In this Note we formulate a q,t-deformation of this n-point function. The key operator used…

We review recent works concerning deformation quantization of abelian supergroups. Indeed, we expose the construction of an induced representation of the Heisenberg supergroup and an associated pseudodifferential calculus by using…

This article serves a two-fold purpose. On the one hand, it is a survey about the classification of finite-dimensional pointed Hopf algebras with abelian coradical, whose final step is the computation of the liftings or deformations of…

We revisit and generalize our previous algebraic construction of the chiral effective action for Conformal Field Theory on higher genus Riemann surfaces. We show that the action functional can be obtained by evaluating a certain Deligne…

In this work, the warped product of Hamilton spaces is introduced and it is shown that these spaces obtain Hamiltonian structure as well. Then, the geometric properties of warped product Hamilton spaces such as their nonlinear connections…

Here we construct spaces of coinvariants for Heisenberg vertex algebras on abelian varieties and show that these globalize to twisted $\mathscr{D}$-modules on the moduli space of abelian varieties. Remarkably, we recover the standard…

We study seminormalization of affine complex varieties. We show that polynomials on the seminormalization correspond to the rational functions which are continuous for the Euclidean topology. We further study this type of functions which…

We study embeddings between reproducing kernel Hilbert spaces $H(K)$ of functions of $d \in \mathbb{N} \cup \{\infty\}$ variables. The kernels $K$ are superpositions of weighted finite tensor products of a fixed univariate kernel. The basic…

A generalized version of the TKNN-equations computing Hall conductances for generalized Dirac-like Harper operators is derived. Geometrically these equations relate Chern numbers of suitable (dual) bundles naturally associated to spectral…

We derive the universal R-matrix of the quantum-deformed enveloping algebra of centrally extended sl(2|2) using Drinfeld's quantum double construction. We are led to enlarging the algebra by additional generators corresponding to an sl(2)…

We propose a covariant holographic c-function, defined directly in a top-down background and constructed from the extrinsic curvature of codimension-two slices of the bulk geometry. The definition does not rely on a special choice of…

Calculations using the (exact) fermionic functional renormalization group are usually truncated at the second order of the corresponding hierarchy of coupled ordinary differential equations. We present a method for the systematic…

Multiparametric families of hypergeometric $\tau$-functions of KP or Toda type serve as generating functions for weighted Hurwitz numbers, providing weighted enumerations of branched covers of the Riemann sphere. A graphical interpretation…