Related papers: Fake degrees of classical Weyl groups

We develop a framework to construct geometric representations of finite groups $G$ through the correspondence between real toric spaces $X^{\mathbb R}$ and simplicial complexes with characteristic matrices. We give a combinatorial…

I calculate characters of certain representations of loop groups based on non simply connected Lie groups. This gives a generalization of the Kac-Weyl character formula.

We calculate the minimal degree for a class of finite complex reflection groups $G(p,p,q)$, for $p$ and $q$ primes and establish relationships between minimal degrees when these groups are taken in a direct product.

We construct natural selfmaps of compact cohomgeneity one manifolds with finite Weyl group and compute their degrees and Lefschetz numbers. On manifolds with simple cohomology rings this yields in certain cases relations between the order…

Unlike classical modular forms, there is currently no general way to implement the computation of Siegel modular forms of arbitrary weight, level and character, even in degree two. There is however, a way to do it in a unified way. After…

In this work, we study the matrix representation of derivations for Mock-Lie algebras with dimensions up to four. Using matrix methods, we examine their structure and properties, showing how these derivations help us better understand the…

By studying the action of the Weyl group of a simple Lie algebra on its root lattice, we construct torsion free subgroups of small and explicitly determined index in a large infinite class of Coxeter groups. One spin-off is the construction…

We construct, using the quantum dilogarithm, a series of *-representations of quantized cluster varieties. This includes a construction of infinite dimensional unitary projective representations of their discrete symmetry groups - the…

We classify, up to isomorphism and up to equivalence, division gradings (by abelian groups) on finite-dimensional simple real algebras. Gradings on finite-dimensional simple algebras are determined by division gradings, so our results give…

We construct multiple Dirichlet series in several complex variables whose coefficients involve quadratic residue symbols. The series are shown to have an analytic continuation and satisfy a certain group of functional equations. These are…

We survey various constructions of finite dimensional projective representations of mapping class groups derived from stated skein algebras.

Finite group theorists have established many formulas that express interesting properties of a finite group in terms of sums of characters of the group. An obstacle to applying these formulas is lack of control over the dimensions of…

We introduce a notion of elliptic differential graded Lie algebra. The class of elliptic algebras contains such examples as the algebra of differential forms with values in endomorphisms of a flat vector bundle over a compact manifold, etc.…

We give information about finite-dimensional Lie algebras and their representations for model building in 4 and 5 dimensions; e.g., conjugacy classes, types of representations, Weyl dimensional formulas, Dynkin indices, quadratic Casimir…

We discuss a classical complexity of finite-dimensional unitary transformations, which can been seen as a computable approximation of classical descriptional complexity of a unitary transformation acting on a set of qubits.

This paper is concerned with rational curves on real classical groups. Our contributions are three-fold: (i) We determine the structure of quadratic rational curves on real classical groups. As a consequence, we completely classify…

For square-integrable genuine Iwahori-spherical representations of central covers, we verify the Hiraga--Ichino--Ikeda formula for their formal degrees. We also compute the Whittaker dimensions of these representations, when their…

We define Weyl functors, global modules for equivariant map Lie superalgebras $(\g \otimes A)^{\Gamma}$, where $\g$ is basic classical $\mathbb{C}$- Lie superalgebra and $A$ is an associative commutative unital $\mathbb{C}$-algebra. Under…

Classical Fourier analysis has an exact counterpart in group theory and in some areas of geometry. Here I'll describe how this goes for nilpotent Lie groups and for a class of Riemannian manifolds closely related to a nilpotent Lie group…

We compute the fundamental groups of all irreducible plane sextics constituting classical Zariski pairs