Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · math/0601728

Holomorphic horospherical transform on non-compactly causal spaces

Simon Gindikin·Bernhard Kroetz·Gestur Olafsson
View original source ↗Read source document ↗Export metadata ↓

Abstract

We develop integral geometry for non-compactly causal symmetric spaces. We define a complex horospherical transform and, for some cases, identify it with a Cauchy type integral.

Explore related subjects

math.RT

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Simon Gindikin, Bernhard Kroetz, Gestur Olafsson. 2006-11-01. Holomorphic horospherical transform on non-compactly causal spaces. https://arxiv.org/abs/math/0601728

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↗