Stein extensions of Riemann symmetric spaces and some generalization

Toshihiko Matsuki

Home/Archive/arXiv

arXiv · math/0208175

Stein extensions of Riemann symmetric spaces and some generalization

Toshihiko Matsuki

View original source ↗Read source document ↗Export metadata ↓

Abstract

It was proved by Huckleberry that the Akhiezer-Gindikin domain is included in the ``Iwasawa domain'' using complex analysis. But we can see that we need no complex analysis to prove it. In this paper, we generalize the notions of the Akhiezer-Gindikin domain and the Iwasawa domain for two associated symmetric subgroups in real Lie groups and prove the inclusion. Moreover, by the symmetry of two associated symmetric subgroups, we also give a direct proof of the known fact that the Akhiezer-Gindikin domain is included in all cycle spaces.

Explore related subjects

math.RT math.AG

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Toshihiko Matsuki. 2002-09-12. Stein extensions of Riemann symmetric spaces and some generalization. https://arxiv.org/abs/math/0208175

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

A uniform trigonometric R-matrix for the exceptional series

The exceptional series is a finite list of points on a projective line with a simple Lie algebra attached to each point. This list of Lie algebras includes the five exceptional Lie algebras. We give a uniform trigonometric $R$-matrix for the exceptional series in the representation $L\oplus I$, where $L$ is the quantum deformation of the adjoint representation and $I$ is the trivial representation. We construct a sixteen dimensional algebra, $A^\square(\mathit2)$, which interpolates the algebras $\mathrm{End}(\otimes^2(L\oplus I))$ and a 287 dimensional algebra, $A^\square(\mathit3)$, which interpolates the algebras $\mathrm{End}(\otimes^3(L\oplus I))$. The $R$-matrix lives in $A^\square(\mathit2)$ and satisfies the Yang-Baxter equation in $A^\square(\mathit3)$; it interpolates the trigonometric $R$-matrices for the points in the exceptional series.

math.RT↗

arXiv2026

Semibricks and wide subcategories in extended module categories

For $d\geq 1$, we define semibricks and wide subcategories in the $d$-extended hearts of bounded $t$-structures on a triangulated category. We show that these semibricks are in bijection with finite-length wide subcategories. When the $d$-extended heart is the $d$-extended module category $d\mbox{-}\mathrm{mod}Λ$ of a finite-dimensional algebra $Λ$ over a field, we define left/right-finite semibricks and left/right-finite wide subcategories in $d\mbox{-}\mathrm{mod}Λ$ and show bijections with $(d+1)$-term simple-minded collections, generalising the bijections between $2$-term simple-minded collections, left/right-finite wide subcategories and left/right-finite semibricks in $\mathrm{mod}Λ$. We use a relation between semibricks and silting complexes to characterise which mutations of $(d+1)$-term silting complexes are again $(d+1)$-term.

math.RT↗

arXiv2026

Incidence algebras and beyond: brick-continuity and generic bricks

We will show that the twelve families of minimally representation-infinite incidence algebras are brick-continuous and admit a generic brick, which will be explicitly constructed. After that, reversing the reduction process between posets, we will show that any representation-infinite incidence algebra is brick-continuous and admits a generic brick, which can be explicitly computed using what will be called ''extension functors''. Lastly, a method to apply these results to a broader class of algebras is given.

math.RT↗