Related papers: Partitions of the wonderful group compactification

Let $R=\oplus_{\Gamma\in\Gamma}R_{\gamma}$ be a $\Gamma$-graded $K$-algebra over a field $K$, where $\Gamma$ is a totally ordered semigroup, and let $I$ be an ideal of $R$. Considering the $\Gamma$-grading filtration $FR$ of $R$ and the…

We use the crystal isomorphisms of the Fock space to describe two maps on partitions and multipartitions which naturally appear in the crystal basis theory for quantum groups in affine type A and in the representation theory of Hecke…

Let $X$ be a nonempty set and $X^{2}$ be the Cartesian square of $X$. Some semigroups of binary relations generated partitions of $X^2$ are studied. In particular, the algebraic structure of semigroups generated by the finest partition of…

The prime graph question asks whether the Gruenberg-Kegel graph of an integral group ring $\mathbb Z G$ , i.e. the prime graph of the normalised unit group of $\mathbb Z G$ coincides with that one of the group $G$. In this note we prove for…

In this article we describe the $G\times G$-equivariant $K$-ring of $X$, where $X$ is a regular compactification of a connected complex reductive algebraic group $G$. Furthermore, in the case when $G$ is a semisimple group of adjoint type,…

We study algebraic (Artin) stacks over $\bar{\mathcal M}_g$ giving a functorial way of compactifying the relative degree $d$ Picard variety for families of stable curves. We also describe for every $d$ the locus of genus $g$ stable curves…

We survey old and new results about the cohomology of the moduli space $A_g$ of principally polarized abelian varieties of genus $g$ and its compactifications. The main emphasis lies on the computation of the cohomology for small genus and…

For a stable curve of genus $g\geq 2$ and simple Lie algebra of type A or C, we show that the conformal blocks algebra $\mathcal{A}$ on $\overline{\mathcal{M}}_g$ is finitely generated and establish an explicit connection to Schmitt and…

Take a bounded symmetric domain $D$ and an arithmetic subgroup $\Gamma$ of ${\rm Aut}(D)$. Take the quotient $D/\Gamma$, compactify and resolve the singularities. We study the fundamental group of the compact complex manifolds that result…

The Gruenberg--Kegel graph (or the prime graph) $\Gamma(G)$ of a finite group $G$ is defined as follows. The vertex set of $\Gamma(G)$ is the set of all prime divisors of the order of $G$. Two distinct primes $r$ and $s$ regarded as…

The assignment of local observables in the vacuum sector, fulfilling the standard axioms of local quantum theory, is known to determine uniquely a compact group G of gauge transformations of the first kind together with a central involutive…

The Gruenberg-Kegel graph (or the prime graph) $\Gamma(G)$ of a finite group $G$ is the graph whose vertex set is the set of prime divisors of $|G|$ and in which two distinct vertices $r$ and $s$ are adjacent if and only if there exists an…

Let $G$ be a nonabelian group, $A\subseteq G$ an abelian subgroup and $n\geqslant 2$ an integer. We say that $G$ has an $n$-abelian partition with respect to $A$, if there exists a partition of $G$ into $A$ and $n$ disjoint commuting…

A closed subgroup $G\subset_uU_N^+$ is called easy when its associated Tannakian category $C_{kl}=Hom(u^{\otimes k},u^{\otimes l})$ appears from a category of partitions, $C=span(D)$ with $D=(D_{kl})\subset P$, via the standard…

A classification is given for factorizations of almost simple groups with at least one factor solvable, and it is then applied to characterize $s$-arc-transitive Cayley graphs of solvable groups, leading to a striking corollary: Except the…

We define new compact matrix quantum groups whose intertwiner spaces are dual to tensor categories of three-dimensional set partitions -- which we call spatial partitions. This extends substantially Banica and Speicher's approach of the so…

An equitable $k$-partition of a graph $G$ is a collection of induced subgraphs $(G[V_1],G[V_2],\ldots,G[V_k])$ of $G$ such that $(V_1,V_2,\ldots,V_k)$ is a partition of $V(G)$ and $-1\le |V_i|-|V_j|\le 1$ for all $1\le i<j\le k$. We prove…

Equivariant compactifications of reductive groups can be described by combinatorial data. On the other hand, equivariant compactifications of the additive group G^n_a are more complicated in at least two respects. First, they often admit…

A wonderful compactification of an orbit under the action of a semi-simple and simply connected group is a smooth projective variety containing the orbit as a dense open subset, and where the added boundary divisor is simple normal…

Let $G$ be a group, $\beta G$ is the Stone-$\check{C}$ech compactification of $\beta G$ endowed with the structure of a right topological semigroup, $G^*=\beta G\setminus G$. Given any subset $A$ of $G$ and $p\in G^*$, we define the…