Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · math/0309314

Equivalence of domains arising from duality of orbits on flag manifolds

Toshihiko Matsuki
View original source ↗Read source document ↗Export metadata ↓

Abstract

In [GM1], we defined a G_R-K_C invariant subset C(S) of G_C for each K_C-orbit S on every flag manifold G_C/P and conjectured that the connected component C(S)_0 of the identity would be equal to the Akhiezer-Gindikin domain D if S is of nonholomorphic type by computing many examples. In this paper, we first prove (in Theorem 1.3 and Corollary 1.4) this conjecture for the open K_C-orbit S on an ``arbitrary'' flag manifold generalizing the result of Barchini. This conjecture for closed S was solved in [WZ1], [WZ2] (Hermitian cases) and [FH] (non-Hermitian cases). We also deduce an alternative proof of this result for non-Hermitian cases from Theorem 1.3.

Explore related subjects

math.RTmath.AG

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Toshihiko Matsuki. 2004-07-30. Equivalence of domains arising from duality of orbits on flag manifolds. https://arxiv.org/abs/math/0309314

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↗