Schur--De-Rham complex and its cohomology
type: Item
instance of: scholarly article
title: Schur--De-Rham complex and its cohomology
zbMATH Open document ID: 1085.18012
published in: Journal of Algebra
publication date: 2005-04-07T00:00:00Z
review text: The author generalizes the notion of De-Rham complex \(S^{d-*} (V)\otimes\Lambda^* (V)\) associated to a finite-dimensional vector space \(V\). The new complex, called Schur-De-Rham complex is associated to a vector space \(V\) and a Young diagram \(\lambda\). This is denoted by \(S_\lambda (V)\). When the \(p\)-core of \(\lambda\) is non-trivial then the complex is exact, where \(p\) is the characteristic of the ground field. The author shows that this is not always the case. The complex has a non-trivial cohomology when the \(p\)-core of \(\lambda\) is trivial. The cohomology of \(S_\lambda(V)\) reflects deep properties of the Young diagram in positive characteristic. The author describes \(H^* (S_\lambda(V))\) for \(\lambda\) with trivial \(p\)-core and \(p\)-quotient consisting of a single diagram.
reviewed by: Goutam Mukherjee
Mathematics Subject Classification ID: 18G35
Mathematics Subject Classification ID: 18E25
Mathematics Subject Classification ID: 16E40
Mathematics Subject Classification ID: 13D25
Mathematics Subject Classification ID: 13D03
Mathematics Subject Classification ID: 05E10
zbMATH DE Number: 2153381
zbMATH Keywords: Young diagram
zbMATH Keywords: Schur complex
zbMATH Keywords: Cohomology
zbMATH Keywords: Koszul complex
author: Marcin Chałupnik
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2004.08.029
OpenAlex ID: W2036821414
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DOI: 10.1016/J.JALGEBRA.2004.08.029
description: scientific article; zbMATH DE number 2153381