相关论文: Extensions of real bounded symmetric domains

Let G be a connected, real, semisimple Lie group contained in its complexification G_C, and let K be a maximal compact subgroup of G. We construct a K_C-G double coset domain in G_C, and we show that the action of G on the K-finite vectors…

The Kr\"otz-Stanton Extension Theorem states that the orbit map of a K-finite vector in a Hilbert representation of a linear Lie group extends to a holomorphic map to a principal fibre bundle over the complex crown domain associated to the…

Let G/H be a pseudo-Riemannian semisimple symmetric space. The tangent bundle T(G/H) contains a maximal G-invariant neighbourhood of the zero section where the adapted complex structure exists. Such neighbourhood is endowed with a canonical…

In this paper we define a distinguished boundary for the complex crowns $\Xi\subeq G_\C /K_\C$ of non-compact Riemannian symmetric spaces $G/K$. The basic result is that affine symmetric spaces of $G$ can appear as a component of this…

For a connected reductive group $G_k$ over an algebraically closed field $k$ of char $\neq 2$ and a fixed point subgroup $K_k$ under an algebraic group involution, we construct a quantization and an integral model of any affine embeddings…

For a real symmetric domain $G_{\mathbb R}/K_{\mathbb R}$, with complexification $G_{\mathbb C}/K_{\mathbb C}$, we introduce the concept of "star-restriction" (a real analogue of the "star-products" for quantization of K\"ahler manifolds)…

Let $\,\Xi\,$ be the crown domain associated with a non-compact irreducible hermitian symmetric space $\,G/K$. We give an explicit description of the unique $\,G$-invariant adapted hyper-K\"ahler structure on $\,\Xi$,$\ $i.$\,$e.$\…

We give a geometric interpretation of the maximal Satake compactification of symmetric spaces $X=G/K$ of noncompact type, showing that it arises by attaching the horofunction boundary for a suitable $G$-invariant Finsler metric on $X$. As…

In our previous paper [GSV2020], we proved that the complementary components of a ring domain in $\mathbb{R}^n$ with large enough modulus may be separated by an annular ring domain and applied this result to boundary correspondence problems…

We quantize the problem considered by Bott-Samelson who applied Morse theory to any compact symmetric space $G/K$ and the associated real flag manifold $G_{\mathbb{R}}/B$ which is a real locus of a complex partial flag variety…

Let $K$ be a local field whose residue field has characteristic $p$ and let $L/K$ be a finite separable totally ramified extension of degree $n=up^{\nu}$. Let $\sigma_1,\dots,\sigma_n$ denote the $K$-embeddings of $L$ into a separable…

Let $ G $ be a connected, simply connected semisimple algebraic group over the complex number field, and let $ K $ be the fixed point subgroup of an involutive automorphism of $ G $ so that $ (G, K) $ is a symmetric pair. We take parabolic…

Let D=G/K be an irreducible Hermitian symmetric domain. Then G is contained in a complexification, and there exists a closed complex subsemigroup, the so-called minimal Olshanskii semigroup, of the complexification characterised by the fact…

Open orbits D of noncompact real forms G_0 acting on flag manifolds of their semisimple complexifications G are considered. The unique orbit C of a maximal compact subgroup K_0 of G_0 in D can be regarded as a point in the (full) cycle…

We prove that for a compact subgroup $H$ of a locally compact Hausdorff group $G$, the following properties are mutually equivalent: (1) $G/H$ is a manifold, (2) $G/H$ is finite-dimensional and locally connected, (3) $G/H$ is locally…

We construct a family of involutions on the space $\mathfrak{gl}_n'(\mathbb C)$ of $n\times n$ matrices with real eigenvalues interpolating the complex conjugation and the transpose. We deduce from it a stratified homeomorphism between the…

There is a known hyperk\"ahler structure on any complexified Hermitian symmetric space $G/K$, whose construction relies on identifying $G/K$ with both a (co)adjoint orbit and the cotangent bundle to the compact Hermitian symmetric space…

Let K/k be purely inseparable extension of characteristic p \textgreater{} 0. By invariants, we characterize the measure of the size of K/k. In particular, we give a necessary and sufficient condition that K/k is of bounded size.…

Flag domains are open orbits of real forms $G_\mathbb{R}$ of complex reductive Lie supergroups $G$ in $G$-flag supermanifolds $Z = G/P$. This thesis discusses three topics from the theory of these flag domains: 1. Measurability(i.e.…

Let $K$ be a normal subgroup of the finite group $H$. To a block of a $K$-interior $H$-algebra we associate a group extension, and we prove that this extension is isomorphic to an extension associated to a block given by the Brauer…