Related papers: The ring of Weyl invariant $E_8$ Jacobi forms

A non-unital generalization of weak bialgebra is proposed with a multiplier-valued comultiplication. Certain canonical subalgebras of the multiplier algebra (named the `base algebras') are shown to carry coseparable co-Frobenius coalgebra…

The main theorem (2.2) consists in two characterizations of isomorphisms of factorial domains in terms of prime or primary rings elements, and unramified, flat or weakly injective affine schemes morphisms. In order to apply this theorem to…

We characterize manifolds which are locally conformally equivalent to either complex projective space or to its negative curvature dual in terms of their Weyl curvature tensor. As a byproduct of this investigation, we classify the…

First and second fundamental theorems are given for polynomial invariants of a class of pseudo-reflection groups (including the Weyl groups of type $B_n$), under the assumption that the order of the group is invertible in the base field.…

Let $R$ be a polynomial ring in $m$ variables over a field of characteristic zero. We classify all rank $n$ twisted generalized Weyl algebras over $R$, up to $\mathbb{Z}^n$-graded isomorphisms, in terms of higher spin 6-vertex…

We define a notion of pseudo-unitarizability for weight modules over a generalized Weyl algebra (of rank one, with commutative coeffiecient ring $R$), which is assumed to carry an involution of the form $X^*=Y$, $R^*\subseteq R$. We prove…

A minimal system of homogeneous generating elements of the invariants algebra for the binary form of degree 7 is calculated.

In the presence of a variable magnetic field, the Weyl pseudodifferential calculus must be modified. The usual modification, based on ``the minimal coupling principle'' at the level of the classical symbols, does not lead to gauge invariant…

We construct all quintic invariants in five variables with simple Non-Abelian finite symmetry groups. These define Calabi-Yau three-folds which are left invariant by the action of A_5, A_6 or PSL_2(11).

The aim of this work is to investigate the structure of some skew twisted algebras, when the coefficient ring is a localization of the polynomial ring over the field of characteristic zero, and an involution is provided. A parallel…

This is the first in a series of papers, where we introduce and study topological spaces that realize the algebras of quasi-invariants of finite reflection groups. Our result can be viewed as a generalization of a well-known theorem of A.…

We compute the small cohomology ring of the Cayley Grassmannian, that parametrizes four-dimensional subalgebras of the complexified octonions. We show that all the Gromov-Witten invariants in the multiplication table of the Schubert classes…

Let $G$ be a simple algebraic group of type $E_6$ over an algebraically closed field of characteristic $p>0$. We determine the submodule structure of the Weyl modul es with highest weight $r\omega_1$ for $0\leq r\leq p-1$, where $\omega_1$…

In the fermionic systems with topologically stable Fermi points the emergent two - component Weyl fermions appear. We propose the topological classification of these fermions based on the two invariants composed of the two - component Green…

Let $\mathbb K$ be an algebraically closed field of characteristic zero. Let $V$ be a module over the polynomial ring $\mathbb K[x,y]$. The actions of $x$ and $y$ determine linear operators $P$ and $Q$ on $V$ as a vector space over $\mathbb…

We develop a pseudo-differential Weyl calculus on nilpotent Lie groups which allows one to deal with magnetic perturbations of right invariant vector fields. For this purpose we investigate an infinite-dimensional Lie group constructed as…

Hilbert's 14th Problem asks the following question. Given a linear representation $ \beta: G \to \operatorname{GL}(\mathbf{V}) $ of a linear algebraic group over a field $ k $ is the ring $ S_{k}(\mathbf{V}^{\ast}) $ a finitely generated $…

Let G be a split real Kac-Moody group of arbitrary type and let K be its maximal compact subgroup, i.e. the subgroup of elements fixed by a Cartan-Chevalley involution of G. We construct non-trivial spin covers of K, thus confirming a…

A theory of cyclic elements in semisimple Lie algebras is developed. It is applied to an explicit construction of regular elements in Weyl groups.

Endomorphisms of Weyl algebras are studied using bimodules. Initially, for a Weyl algebra over a field of characteristic zero, Bernstein's inequality implies that holonomic bimodules finitely generated from the right or left form a monoidal…