Related papers: Elementary covering numbers in odd-dimensional uni…

In the conventional formulation of N=1 supersymmetry, a vector multiplet is supposed to be in the adjoint representation of a given gauge group. We present a new formulation with a vector multiplet in the non-adjoint representation of SO(N)…

If $N \subset P,Q \subset M$ are type II_1 factors with $N' \cap M = C id$ and $[M:N]$ finite we show that restrictions on the standard invariants of the elementary inclusions $N \subset P$, $N \subset Q$, $P \subset M$ and $Q \subset M$…

A central problem in discrete geometry, known as Hadwiger's covering problem, asks what the smallest natural number $N\left(n\right)$ is such that every convex body in ${\mathbb R}^{n}$ can be covered by a union of the interiors of at most…

We prove a uniqueness result for finite-dimensional representations of the Kauffman skein algebra $\mathcal{S}_A(S)$ of a surface $S$, when $A$ is a root of unity and when the surface $S$ is a sphere with at most four punctures or a torus…

An automorphism of an algebraic surface $S$ is called cohomologically (numerically) trivial if it acts identically on the second $l$-adic cohomology group (this group modulo torsion subgroup). Extending the results of S. Mukai and Y.…

The elementary action of symplectic and orthogonal groups on unimodular rows of length $2n$ is transitive for $2n \geq \max(4, d+2)$ in the symplectic case, and $2n \geq \max(6, 2d+4)$ in the orthogonal case, over monoid rings $R[M]$, where…

Let $E$ be a two-dimensional \'etale algebra over a non-Archimedean local field $K$ of characteristic zero. We show that the unitary group of a non-degenerate hermitian lattice over $E$ is generated by symmetries and rescaled Eichler…

Every almost Hermitian structure $(g,J)$ on a four-manifold $M$ determines a hypersurface $\Sigma_J$ in the (positive) twistor space of $(M,g)$ consisting of the complex structures anti-commuting with $J$. In this note we find the…

For each $1\leq i \le n$, let $k_i\geq 1$ and let $\Delta_i$ be a set of vertices of a non-degenerate simplex of $k_i+1$ points in $\mathbb{R}^{k_i+1}$. If $A\subseteq [0,1]^{k_1+1}\times \cdots \times [0,1]^{k_n+1}$ is a Lebesgue…

A subset $S$ of the alternating group on $n$ points is {\it intersecting} if for any pair of permutations $\pi,\sigma$ in $S$, there is an element $i\in \{1,\dots,n\}$ such that $\pi(i)=\sigma(i)$. We prove that if $S$ is intersecting, then…

In this paper we study the lower triangular matrix $\mathbb{K}$-algebra $\Lambda:=\left[\begin{smallmatrix} T & 0 \\ M & U \end{smallmatrix}\right],$ where $U$ and $T$ are basic $\mathbb{K}$-algebras with enough idempotents and $M$ is an…

In the present paper we prove a weak form of sandwich classification for the overgroups of the subsystem subgroup $E(\Delta,R)$ of the Chevalley group $G(\Phi,R)$ where $\Phi$ is a simply laced root sysetem and $\Delta$ is its sufficiently…

A transitive group $G$ of permutations of a set $\Omega$ is primitive if the only $G$-invariant equivalence relations on $\Omega$ are the trivial and universal relations. If $\alpha \in \Omega$, then the orbits of the stabiliser $G_\alpha$…

Given a compact orientable surface $\Sigma$, let $\Cal S(\Sigma)$ be the set of isotopy classes of essential simple loops on $\Sigma$. We determine a complete set of relations for a function from $\Cal S(\Sigma)$ to $\bold Z$ to be a…

The circular descent of a permutation $\sigma$ is a set $\{\sigma(i)\mid \sigma(i)>\sigma(i+1)\}$. In this paper, we focus on the enumerations of permutations by the circular descent set. Let $cdes_n(S)$ be the number of permutations of…

Let $X$ be a complex $K3$ surface with an effective action of a group $G$ which preserves the holomorphic symplectic form. Let $$ Z_{X,G}(q) = \sum_{n=0}^{\infty} e\left(\operatorname{Hilb}^{n}(X)^{G} \right)\, q^{n-1} $$ be the generating…

We construct a full strongly exceptional collection in the triangulated category of graded matrix factorizations of a polynomial associated to a non-degenerate regular system of weights whose smallest exponents are equal to -1. In the…

A set of permutations of $\{1,2,\dots,n\}$ is $t$-intersecting if any two permutations agree on at least $t$ inputs. A recent work by Kupavskii, in the spirit of the Erd\H{o}s-Ko-Rado Theorem, shows that for all $t\leq…

Let $$ F(x, y) = \prod\limits_{k = 0}^{n - 1}(\delta_kx - \gamma_ky) $$ be a binary form of degree $n \geq 1$, with complex coefficients, written as a product of $n$ linear forms in $\mathbb C[x, y]$. Let $$ h_F = \prod\limits_{k = 0}^{n -…

Let $K$ be a local field whose residue field has characteristic $p$ and let $L/K$ be a finite separable totally ramified extension of degree $n=up^{\nu}$. Let $\sigma_1,\dots,\sigma_n$ denote the $K$-embeddings of $L$ into a separable…