Related papers: Fake degrees of classical Weyl groups

We describe the isomorphism classes of infinite-dimensional graded Lie algebras of maximal class, generated by elements of weight one, over fields of odd characteristic.

We classify closed abelian subgroups of the automorphism group of any compact classical simple Lie algebra whose centralizer has the same dimension as the dimension of the subgroup, and describe Weyl groups of maximal abelian subgroups.

In this paper we investigate weak polynomial identities for the Weyl algebra $\mathsf{A}_1$ over an infinite field of arbitrary characteristic. Namely, we describe weak polynomial identities of the minimal degree, which is three, and of…

The Lie algebras over the algebra of dual numbers are introduced and investigated.

We discuss the homological algebra of representation theory of finite dimensional algebras and finite groups. We present various methods for the construction and the study of equivalences of derived categories: local group theory, geometry…

We study the class of idempotent-generated pseudo-composition algebras, which is a subclass of the family of axial algebras. More specifically, we utilise the group-algebra correspondence, natural to the axial framework in order to study…

Using generating functions, we enumerate regular semisimple conjugacy classes in the finite classical groups. For the general linear, unitary, and symplectic groups this gives a different approach to known results; for the special…

We study the conjugacy classes of the classical affine groups. We derive generating functions for the number of classes analogous to formulas of Wall and the authors for the classical groups. We use these to get good upper bounds for the…

This survey is about the fundamentals of the theory of finite dimensional Lie groups over the field of real numbers. The notion of the tangent space of a manifold at a point is considered to be defined via the well known chart and vector…

In this paper we introduce the classical and quantum covariant Weil algebras. Covariant Weil algebras are simultaneous generalizations of Weil algebras and family algebras. We will define differentials, Lie derivatives and contractions on…

We compute the noncommutative deformations of a family of modules over the first Weyl algebra. This example shows some important properties of noncommutative deformation theory that separates it from commutative deformation theory.

A fake quadric is a smooth projective surface that has the same rational cohomology as a smooth quadric surface but is not biholomorphic to one. We provide an explicit classification of all irreducible fake quadrics according to the…

In this paper we describe the polynomial identities of degree 4 for a certain subspace of the Weyl algebra A_1 over an infinite field of arbitrary characteristic.

We use fermionic representations to obtain a class of BC$_{{}_{\text N}}$-graded Lie algebras coordinatized by quantum tori with nontrivial central extensions.

We deduce decompositions of natural representations of general linear groups and symmetric groups from combinatorial bijections involving tableaux. These include some of Howe's dualities, Gelfand models, the Schur-Weyl decomposition of…

A catalogue of explicit realizations of representations of (super) Lie algebras and quantum algebras in Fock space is presented.

In this paper we describe a new method of calculation of master integrals based on the solution of systems of difference equations in one variable. An explicit example is given, and the generalization to arbitrary diagrams is described. As…

Super Weyl group plays an important role in the study of representations of basic classical Lie superalgebras. The Coxeter graphs for super Weyl groups of basis classical Lie superalgebras have been given in \cite{CLS}, where the authors…

Finite-dimensional subalgebras of a Lie algebra of smooth vector fields on a circle, as well as piecewise-smooth global transformations of a circle on itself, are considered. A canonical forms of realizations of two- and three-dimensional…

We give a general definition of classical and quantum groups whose representation theory is "determined by partitions" and study their structure. This encompasses many examples of classical groups for which Schur-Weyl duality is described…