Related papers: Analytic factorization of Lie group representation…

An algebraic group is called semi-reductive if it is a semi-direct product of a reductive subgroup and the unipotent radical. Such a semi-reductive algebraic group naturally arises and also plays a key role in the study of modular…

Let $(G,\tau)$ be a finite-dimensional Lie group with an involutive automorphism $\tau$ of $G$ and let $\mathfrak g = \mathfrak h \oplus \mathfrak q $ be its corresponding Lie algebra decomposition. We show that every non-degenerate…

We consider the infinite-dimensional Lie group $\mathfrak G$ which is the semidirect product of the group of compactly supported diffeomorphisms of a Riemannian manifold $X$ and the commutative multiplicative group of functions on $X$. The…

A discrete version of Lagrangian reduction is developed in the context of discrete time Lagrangian systems on $G\times G$, where $G$ is a Lie group. We consider the case when the Lagrange function is invariant with respect to the action of…

We construct the well-known decomposition of the Lie algebra $\mathfrak{e}_8$ into representations of $\mathfrak{e}_6\oplus\mathfrak{su}(3)$ using explicit matrix representations over pairs of division algebras. The minimal representation…

If $G$ is a compact Lie group endowed with a left invariant metric $g$, then $G$ acts via pullback by isometries on each eigenspace of the associated Laplace operator $\Delta_g$. We establish algebraic criteria for the existence of left…

We prove that if $\frak{g}^{\prime}$ is a contraction of a Lie algebra $\frak{g}$ then the number of functionally independent invariants of $\frak{g}^{\prime}$ is at least that of $\frak{g}$. This allows to determine explicitly the number…

For any semisimple Lie algebra $\mathfrak{g}$, the universal enveloping algebra of the infinite-dimensional pro-nilpotent Lie algebra $\mathfrak{g}_-:=\mathfrak{g}\otimes t^{-1}\mathbb{C}[t^{-1}]$ contains a large commutative subalgebra…

Given a linear representation $\rho : \mathfrak{g} \longrightarrow \mathfrak{g}\ell(V)$ of a Lie algebra $\mathfrak{g}$, one can define a linear representation $\rho_m : \mathfrak{g}_m \longrightarrow \mathfrak{g}\ell(V^m)$ of the…

As announced in [12], we develop a calculus of Fourier integral G-operators on any Lie groupoid G. For that purpose, we study convolability and invertibility of Lagrangian conic submanifolds of the symplectic groupoid T * G. We also…

During the last decades algebraization of space turned out to be a promising tool at the interface between Mathematics and Theoretical Physics. Starting with works by Gel'fand-Kolmogoroff and Gel'fand-Naimark, this branch developed as from…

We study families of analytic $p$-divisible groups over adic spaces $S$ defined over $\mathbb{Q}_p$. We prove an equivalence between such families and Hodge-Tate triples, generalizing a theorem of Fargues. For a perfectoid space $S$, we…

A space of entire functions of several complex variables rapidly decreasing on ${\mathbb R}^n$ and such that their growth along $i{\mathbb R}^n$ is majorized with a help of a family of weight functions is considered in the paper. For this…

Let $\mathfrak{g}$ be a nilpotent Lie algebra which is also regarded as a homogeneous Lie group with the Campbell-Hausdorff multiplication. This allows to define a generalized multiplication $f \# g = (f^{\vee} * g^{\vee})^{\wedge}$ of two…

We prove that the spaces of smooth and ultradifferentiable vectors associated with a representation of a real Lie group on a Fr\'{e}chet space $E$ are quasinormable if $E$ is so. A similar result is shown to hold for the linear topological…

We construct by geometric methods a noncommutative model E of the algebra of regular functions on the universal (2-fold) cover M of certain nilpotent coadjoint orbits O for a complex simple Lie algebra g. Here O is the dense orbit in the…

Let $G$ be a real reductive connected Lie group and $\sigma$ an involution of $G$. Let $H$ denote the identity component of the group of fixed points of $\sigma$, $\mathfrak g$ the Lie algebra of $G$ and $\mathfrak q$ the -1 eigenspace of…

Normal elements (or multipliers) of the C* algebra of a certain class of locally compact groupoids admit a natural faithful representation as normal operators on the $L^2$-space of a dense orbit of the groupoid. We prove norm estimates on…

Let A be a dense Frechet *-subalgebra of a C*-algebra B. (We do not require Frechet algebras to be m-convex.) Let G be a Lie group, not necessarily con- nected, which acts on both $A$ and B by *-automorphisms, and let \s be a sub-…

Let $X$ be a smooth scheme with an action of a reductive algebraic group $G$ over an algebraically closed field $k$ of characteristic zero. We construct an action of the extended affine Braid group on the $G$-equivariant absolute derived…