Related papers: Orders of Finite Reductive Monoids

We give an efficient algorithm for the enumeration up to isomorphism of the inverse semigroups of order n, and we count the number S(n) of inverse semigroups of order n<=15. This improves considerably on the previous highest-known value…

We give a general construction for finite dimensional representations of $U_q(\hat{\G})$ where $\hat{\G}$ is a non-twisted affine Kac-Moody algebra with no derivation and zero central charge. At $q=1$ this is trivial because…

For a group G we consider the set of natural numbers n for which the nth cohomology functor of G commutes with filtered colimit systems of coefficient modules. We find that for the large class of hierarchically decomposable groups there is…

We prove that the lexicographic, degree lexicographic and the degree reverse lexicographic orders for monomials in $R_n=K[X_1,...X_n]$ are uniquely determined by their induced orderings, (i.e. their restrictions to $R_{n,i}=K[X_1,...,…

We obtain an asymptotic upper bound for the product of the $p$-parts of the orders of certain composition factors of a finite group acting completely reducibly and faithfully on a finite vector space of order divisible by a prime $p$. An…

We study the Betti tables of reducible algebraic curves with a focus on connected line arrangements and provide a general formula for computing the quadratic strand of the Betti table for line arrangements that satisfy certain hypotheses.…

We consider finite W-algebras U(g,e) associated to even multiplicity nilpotent elements in classical Lie algebras. We give a classification of finite dimensional irreducible U(g,e)-modules with integral central character in terms of the…

An $integral$ of a group $G$ is a group $H$ whose derived group (commutator subgroup) is isomorphic to $G$. This paper discusses integrals of groups, and in particular questions about which groups have integrals and how big or small those…

Every nonabelian finite simple group of rank $n$ over a field of size $q$, with the possible exception of the Ree groups $^2G_2(3^{2e+1})$, has a presentation with a bounded number of generators and relations and total length $O(\log n…

Commutative totally ordered monoids abound, number systems for example. When the monoid is not assumed commutative, one may be hard pressed to find an example. One suggested by Professor Orr Shalit are the countable ordinals with addition.…

We study finite dimensional algebras that appear as fibers of quantum orders over a given point of variety of center. We present the formula for the number of irreducible representations and check it for it for the algebra of twisted…

For every finite rank k, k>1, we explicitly construct (2k)! left orders on the free group F_k of rank k. Each order is induced by a word of length 2k in which each generator of F_k and its inverse appear exactly once. For each of these…

We construct a simplified resolution for the trivial G-module Z, where G is a finite abelian group, and compare it with the standard resolution. We use it to calculate cohomologies of irreducible G-lattices and their duals.

We classify finite-dimensional irreducible highest weight modules of generalized quantum groups whose positive part is infinite dimensional and has a Kharchenko's PBW basis with an irreducible finite positive root system.

We give new, explicit and asymptotically sharp, lower bounds for dimensions of irreducible modular representations of finite symmetric groups.

This paper is devoted to the study of metric subregularity and strong subregularity of any positive order $q$ for set-valued mappings in finite and infinite dimensions. While these notions have been studied and applied earlier for $q=1$…

Radical subgroups play an important role in both finite group theory and representation theory. This is the first of a series of papers of ours in classifying radical $p$-subgroups of finite reductive groups and in verifying the inductive…

The paper studies modular reduction techniques for abstract regular and chiral polytopes, with two purposes in mind: first, to survey the literature about modular reduction in polytopes; and second, to apply modular reduction, with moduli…

In this paper, we prove that infinite cancellative finitely generated hyperbolic monoids never contain $\mathbb N\times\mathbb N$ as a submonoid but that they contain an element of infinite order and, if they are elementary, then they also…

Say that a cone is a commutative monoid in which x+y=0 implies that x=y=0. We show that cones (resp. simple cones) of many kinds order-embed or even embed unitarily into refinement cones (resp. simple refinement cones) of the same kind,…