Related papers: A universal formula for the volume of compact Lie …

A 'mass formula' is a formula involving a sum of reciprocals of automorphism groups orders. We provide several such formulae, e.g. ones involving covering groups of finite groups. Others generalize a formula of P.Hall, repalcing the class…

The coefficients occurring in summation formulae of the Lubbock type are shown to be generalised Bernoulli polynomials which turn up in subdivision questions such as quantum field theory around a conical singularity and on spherical lunes.…

There is an elegant expression for the volume of hypercube $[0,1]^n$ clipped by a single hyperplane. In the article the formula is generalized to the case of more than one hyperplane. An important foundation for the result is Lawrence's…

Let G be a compact connected Lie group and H, the centralizer of a one-parameter subgroup in G. Combining the ideas of Bott-Samelson resulotions of Schubert varieties and the enumerative formula on a twisted products of 2-spheres obatained…

It is proved that if $u_1,\ldots, u_n$ are vectors in ${\Bbb R}^k, k\le n, 1 \le p < \infty$ and $$r = ({1\over k} \sum ^n_1 |u_i|^p)^{1\over p}$$ then the volume of the symmetric convex body whose boundary functionals are $\pm u_1,\ldots,…

There exists, in general, no unique definition of the size (volume, area, etc., depending on dimension) of a soliton. Here we demonstrate that the geometric volume (area etc.) of a soliton is singled out in the sense that it exactly…

We propose a general framework to contract unitary dual of Lie groups via holomorphic quantization of their co-adjoint orbits. The sufficient condition for the contractability of a representation is expressed via cocycles on coadjoint…

This paper develops a unified framework for estimating the volume of a set in $\mathbb{R}^d$ based on observations of points uniformly distributed over the set. The framework applies to all classes of sets satisfying one simple axiom: a…

Let $G$ be a simple Lie Group with finite center, and let $K\subset G$ be a maximal compact subgroup. We say that $G$ is a Lie group of tube type if $G/K$ is a hermitian symmetric space of tube type. For such a Lie group $G$, we can find a…

In this note, we prove that the universal affine vertex algebra associated with a simple Lie algebra $\mathfrak{g}$ is simple if and only if the associated variety of its unique simple quotient is equal to $\mathfrak{g}^*$. We also derive…

The main thrust of present note is a volume formula for hyperbolic surface bundle with the fundamental group G. The novelty consists in a purely algebraic approach to the above problem. Initially, we concentrate on the Baum-Connes morphism…

Let $U$ be an algebraic subgroup of the group of $n\times n$ upper-triangular matrices with units on the diagonal over a finite field of large enough characteristic, and $\mathfrak{n}$ be the Lie algebra of $U$. The main tool in…

Let $G$ be the adjoint group of a real simple Lie algebra $\mathfrak{g}_0$ equal either $\mathfrak{s}\mathfrak{u}(n,1)$ or $\mathfrak{s}\mathfrak{o}(n,1),$ $K$ its maximal compact subgroup, ${\cal U}(\mathfrak{g})$ the universal enveloping…

A generalized hyperbolic tetrahedra is a polyhedron (possibly non-compact) with finite volume in hyperbolic space, obtained from a tetrahedron by the polar truncation at the vertices lying outside the space. In this paper it is proved that…

This article studies the volume of compact quotients of reductive homogeneous spaces. Let $G/H$ be a reductive homogeneous space and $\Gamma$ a discrete subgroup of $G$ acting properly discontinuously and cocompactly on $G/H$. We prove that…

The Wigner-Eckart theorem is a well known result for tensor operators of SU(2) and, more generally, any compact Lie group. This paper generalises it to arbitrary Lie groups, possibly non-compact. The result relies on knowledge of recoupling…

We investigate Beurling-Fourier algebras, a weighted version of Fourier algebras, on various Lie groups focusing on their spectral analysis. We will introduce a refined general definition of weights on the dual of locally compact groups and…

In this paper we define a two-variable, generic Hecke algebra, H, for each complex reflection group G(b,1,n). The algebra H specializes to the group algebra of G(b,1,n) and also to an endomorphism algebra of a representation of GL(n,q)…

In this paper, we prove an existence result for K\"ahler-Einstein metrics on $\mathbb Q$-Fano compactifications of Lie groups. As an application, we classify $\mathbb Q$-Fano compactifications of $SO_4(\mathbb C)$ which admit a…

In this paper we study a group theoretical generalization of the well-known Gauss's formula that uses the generalized Euler's totient function introduced in [11].