The canonical combinatorial sheaf associated to an involution of a semisimple adjoint group. Case \(A_ n\)
type: Item
instance of: scholarly article
title: The canonical combinatorial sheaf associated to an involution of a semisimple adjoint group. Case \(A_ n\)
zbMATH Open document ID: 0794.20056
DOI: 10.1007/BF02571675
author: Renata Scognamillo
published in: Mathematische Zeitschrift
publication date: 1994-08-25T00:00:00Z
full work available at URL: https://eudml.org/doc/174504
review text: Let \(G\) be a semisimple adjoint group over \(\mathbb{C}\) with involution \(\sigma\) and consider an associated restricted root system with basis of simple roots \(\Sigma\). The author defines a combinatorial sheaf of rings \({\mathcal F}_ G^ \sigma\) on the finite simplicial complex \(({\mathcal V},{\mathcal S})= (\Sigma,\{\text{subsets in }\Sigma\})\). As a consequence of some results of \textit{E. Bifet}, \textit{C. de Concini} and \textit{C. Procesi} [Adv. Math. 82, No. 1, 1-34 (1990; Zbl 0743.14018)] such a sheaf actually determines the rational \(G\)-equivariant cohomology ring of any good compactification of the symmetric variety \(G/G^ \sigma\). The author describes explicitly \({\mathcal F}_ G^ \sigma\) for the case \(G=\text{PGl}(n,\mathbb{C})\).
Mathematics Subject Classification ID: 20G10
Mathematics Subject Classification ID: 20G20
Mathematics Subject Classification ID: 14L30
zbMATH DE Number: 549750
zbMATH Keywords: semisimple adjoint group over \(\mathbb{C}\)
zbMATH Keywords: restricted root system
zbMATH Keywords: combinatorial sheaf
zbMATH Keywords: finite simplicial complex
zbMATH Keywords: rational \(G\)-equivariant cohomology ring
zbMATH Keywords: symmetric variety
MaRDI profile type: Publication
cites work: Cohomology of regular embeddings
cites work: Q3897665
OpenAlex ID: W2083922444
description: scientific article; zbMATH DE number 549750