Polyhedra in the scheme space and the canonical basis in irreducible representations of \({\mathfrak gl}_ 3\)
type: Item
instance of: scholarly article
title: Polyhedra in the scheme space and the canonical basis in irreducible representations of \({\mathfrak gl}_ 3\)
zbMATH Open document ID: 0606.17006
DOI: 10.1007/BF01078396
publication date: 1985-01-01T00:00:00Z
review text: An interesting geometric interpretation is given for the multiplicities in the decomposition of a tensor product of two irreducible finite- dimensional \({\mathfrak gl}_ n\)-modules into irreducible components. The interpretation is given in terms of some convex polyhedron in the Gel'fand-Tsetlin scheme space. An application is given to the classical Clebsch-Gordan coefficients.
Mathematics Subject Classification ID: 17B10
Mathematics Subject Classification ID: 17B20
Mathematics Subject Classification ID: 22E46
zbMATH DE Number: 3979311
zbMATH Keywords: decomposition into irreducible modules
zbMATH Keywords: canonical basis for \({\mathfrak gl}_ 3\)
zbMATH Keywords: multiplicities
zbMATH Keywords: tensor product
zbMATH Keywords: \({\mathfrak gl}_ n\)-modules
zbMATH Keywords: Gel'fand-Tsetlin scheme
zbMATH Keywords: Clebsch-Gordan coefficients
author: I. M. Gel'fand
author: Andrei Zelevinsky
MaRDI profile type: Publication
cites work: Q3947818
cites work: Special bases for \(S_n\) and \(\text{GL}(n)\)
cites work: Q5635639
cites work: Q5795544
full work available at URL: https://doi.org/10.1007/bf01078396
OpenAlex ID: W1970127949
published in: Functional Analysis and Its Applications
description: scientific article; zbMATH DE number 3979311