Related papers: Strata of Weyl groups
We classify the types of root systems $R$ in the rings of integers of number fields $K$ such that the Weyl group $W(R)$ lies in the group $\mathcal L(K)$ generated by ${\rm Aut} (K)$ and multiplications by the elements of $K^*$. We also…
We study the new basis of the (complexified) Grothendieck group of unipotent representations of a split reductive group over a finite field. For exceptional types we use a definition of the new basis which differs from the earlier one.
We show that the higher-order Weyl algebras over a field of characteristic zero, which are formally rigid as associative algebras, can be formally deformed in a nontrivial way as hom-associative algebras. We also show that these…
We define and study a class of $\mathcal{N}=2$ vertex operator algebras $\mathcal{W}_{\mathcal{\mathsf{G}}}$ labelled by complex reflection groups. They are extensions of the $\mathcal{N}=2$ super Virasoro algebra obtained by introducing…
The `Weyl symmetric functions' studied here naturally generalize classical symmetric (polynomial) functions, and `Weyl bialternants,' sometimes also called Weyl characters, analogize the Schur functions. For this generalization, the…
Equivariant map algebras are Lie algebras of algebraic maps from a scheme (or algebraic variety) to a target finite-dimensional Lie algebra (in the case of the current paper, we assume the latter is a simple Lie algebra) that are…
Finite groups with given systems of permuteral and strongly permuteral subgroups are studied. New characterizations of w-supersoluble and supersoluble groups are received.
We define an algebraic group over a group $G$ to be a variety - that is, a subset of $G^d$ defined by equations over $G$ - endowed with a group law whose coordinates can be expressed as word maps. In the case where $G$ is a torsion-free…
Over a field $F$ of any characteristic, for a commutative associative algebra $A$ with an identity element and for the polynomial algebra $F[D]$ of a commutative derivation subalgebra $D$ of $A$, the associative and the Lie algebras of Weyl…
We use the author's combinatorial theory of full heaps (defined in math.QA/0605768) to categorify the action of a large class of Weyl groups on their root systems, and thus to give an elementary and uniform construction of a family of…
We introduce a notion of a root groupoid as a replacement of the notion of Weyl group for (Kac-Moody) Lie superalgebras. The objects of the root groupoid classify certain root data, the arrows are defined by generators and relations. As an…
This note presents a procedure to determine the reduction of the irreducible and the induced characters of the symmetric group in terms of the irreducible and induced characters of the hyperoctahedral group Key Words: Symmetric Group,…
For a semisimple Lie algebra admitting a good enumeration, we prove a parametrization for the elements in its Weyl group. As an application, we give a coordinate-free comparison between the crystal graph description (when it is known) and…
Given an algebraically closed field $\Bbbk$ of characteristic zero, a Lie superalgebra $\mathfrak{g}$ over $\Bbbk$ and an associative, commutative $\Bbbk$-algebra $A$ with unit, a Lie superalgebra of the form $\mathfrak{g} \otimes_\Bbbk A$…
Generalized strata of meromorphic differentials are loci within the usual strata of differentials where certain sets of residues sum to zero. They naturally appear in the boundary of the multi-scale compactification of the usual strata. The…
We extend the classification of finite Weyl groupoids of rank two. Then we generalize these Weyl groupoids to `reflection groupoids' by admitting non-integral entries of the Cartan matrices. This leads to the unexpected observation that the…
On the transversals of a subgroup of a group, using the binary operation of the group, structural mappings are defined. Based on these mappings, the notion of the hypergroup over the group is introduced, which generalizes the notion of the…
In this article, we show that conjugacy classes of classical Weyl groups $W(B_{n})$ and $W(D_{n})$ are of $\textit{type D}$. Consequently, we obtain that Nichols algebras of irreducible Yetter-Drinfeld modules over the classical Weyl groups…
This paper is a contribution to the study of the geometry of algebras related the Weyl groupoid initiated in \cite{M22}. The Nullstellensatz gives a bijection between radical ideals of such an algebra and their zero loci, the superalgebraic…
We investigate arrangements of hyperplanes whose normal vectors are given by connected subgraphs of a fixed graph. These include the resonance arrangement and certain ideal subarrangements of Weyl arrangements. We characterize those which…