Related papers: Zero fibers of quaternionic quotient singularities

The main purpose of this paper is to investigate the zero-divisors of semigroups with zero and semirings and in particular, to discuss eversible and reversible semigroups and semirings. We also introduce a new ring-like algebraic structure…

In this paper, we prove the integrality conjecture for quotient stacks arising from weakly symmetric representations of reductive groups. Our main result is a decomposition of the cohomology of the stack into finite-dimensional components…

Let $V$ be a finite dimensional complex vector space and $W\subseteq \GL(V)$ be a finite complex reflection group. Let $V^{\reg}$ be the complement in $V$ of the reflecting hyperplanes. We prove that $V^{\reg}$ is a $K(\pi,1)$ space. This…

For any complex reflection group $G=G(m,p,n)$, we prove that the $G$-invariants of the division ring of fractions of the $n$:th tensor power of the quantum plane is a quantum Weyl field and give explicit parameters for this quantum Weyl…

In this paper we prove a strong version of the Hilbert Nullstellensatz in the ring $\mathbb H[q_1,\ldots,q_n]$ of slice regular polynomials in several quaternionic variables. Our proof deeply depends on a detailed analysis of the common…

For any finite reflection group $W$ on $\mathbb{R}^{N}$ and any irreducible $W$-module $V$ there is a space of polynomials on $\mathbb{R}^{N}$ with values in $V$. There are Dunkl operators parametrized by a multiplicity function, that is,…

If E is a non-isotrivial elliptic curve over a global function field F of odd characteristic we show that certain Mordell-Weil groups of E have 1-dimensional eigenspace relative to a fixed complex ring class character provided that the…

We define a linear structure on Grothendieck's arithmetic fundamental group $\pi_1(X, x)$ of a scheme $X$ defined over a field $k$ of characteristic 0. It allows us to link the existence of sections of the Galois group ${\rm Gal}(\bar k/k)$…

We prove that the quotients of the group algebra of the braid group on 3 strands by a generic quartic and quintic relation respectively, have finite rank. This is a special case of a conjecture by Brou\'{e}, Malle and Rouquier for the…

We survey recent results on the representation theory of symplectic reflection algebras, focusing particularly on connections with symplectic quotient singularities and their resolutions, spaces of representations of quivers, and on…

The cyclic sieving phenomenon was defined by Reiner, Stanton, and White in a 2004 paper. Let X be a finite set, C be a finite cyclic group acting on X, and f(q) be a polynomial in q with nonnegative integer coefficients. Then the triple…

Consider an affine Coxeter group $W$ acting by isometries on the Euclidean space $\mathbb{R}^n$, and the arrangement of its reflection hyperplanes. The fundamental group of the complement $Y_W$ of the complexification of this arrangement in…

We prove new structural results for the rational homotopy type of the classifying space $B\operatorname{aut}(X)$ of fibrations with fiber a simply connected finite CW-complex $X$. We first study nilpotent covers of $B\operatorname{aut}(X)$…

Let g be a complex semisimple Lie algebra, and f : g --> g/G the adjoint quotient map. Springer theory of Weyl group representations can be seen as the study of the singularities of f. We give a generalization of Springer theory to visible,…

This paper studies three results that describe the structure of the super-coinvariant algebra of pseudo-reflection groups over a field of characteristic $0$. Our most general result determines the top component in total degree, which we…

We employ the slice spectral sequence, the motivic Steenrod algebra, and Voevodsky's solutions of the Milnor and Bloch-Kato conjectures to calculate the hermitian $K$-groups of rings of integers in number fields. Moreover, we relate the…

The description of irreducible representations of a group G can be seen as a question in harmonic analysis; namely, decomposing a suitable space of functions on G into irreducibles for the action of G x G by left and right multiplication.…

Given a representation N of a reductive group G, Braverman-Finkelberg-Nakajima have defined a remarkable Poisson variety called the Coulomb branch. Their construction of this space was motivated by considerations from 3d gauge theories and…

We consider morphisms $\pi: X \to \mathbb{P}^1$ of smooth projective varieties over $\mathbb{C}$. We show that if $\pi$ has at most one singular fibre, then $X$ is uniruled and $\pi$ admits sections. We reach the same conclusions, but with…

We study the coarse quotient $\mathfrak{t}^*//W^{\text{aff}}$ of the affine Weyl group $W^{\text{aff}}$ acting on a dual Cartan $\mathfrak{t}^*$ for some semisimple Lie algebra. Specifically, we classify sheaves on this space via a…