Young-derived sequences of \(S_ n\)-characters
type: Item
instance of: scholarly article
title: Young-derived sequences of \(S_ n\)-characters
zbMATH Open document ID: 0819.20013
published in: Advances in Mathematics
publication date: 1995-08-24T00:00:00Z
review text: For any sequence \(\psi = \{\psi_ n\}_{n \geq 0}\) of characters of the symmetric groups \(S_ n\), \(n = 0,1,2, \dots\), the author constructs the Young-derived sequence \[ y(\psi) = \{y_ n(\psi)\}_{n \geq 0} =\biggl\{\sum_{j=0}^ n \psi_ j \widehat{\otimes} \chi_{(n- j)}\biggr\}_{n \geq 0}, \] where \(\chi_{(k)}\) is the trivial \(S_ k\)- character and \(\widehat{\otimes}\) denotes the outer product expressed in terms of the Young rule. The aim of the paper is to analyze the relations between the sequences \(\psi\) and \(y(\psi)\). It turns out that the Young- derived sequences arise naturally in representation theory, combinatorics and the theory of algebras with polynomial identities. The author studies the asymptotic behaviour of the degrees of the characters \(\psi_ n\) and \(y_ n(\psi)\). Among other results he obtains an integration formula which extends some Macdonald type integrals and he evaluates some of these integrals. The author also gives a method which approximately determines the sequence \(\psi\) from the sequence \(y(\psi)\). Finally he applies this machinery to the cocharacters and codimensions of the ordinary and trace polynomial identities of matrix algebras.
reviewed by: Vesselin Drensky
Mathematics Subject Classification ID: 20C30
Mathematics Subject Classification ID: 05E10
Mathematics Subject Classification ID: 16R30
Mathematics Subject Classification ID: 15A72
Mathematics Subject Classification ID: 16R10
zbMATH DE Number: 638526
zbMATH Keywords: outer tensor products
zbMATH Keywords: characters of symmetric groups
zbMATH Keywords: degrees of characters
zbMATH Keywords: outer products
zbMATH Keywords: Young rule
zbMATH Keywords: Young-derived sequences
zbMATH Keywords: algebras with polynomial identities
zbMATH Keywords: asymptotic behaviour
zbMATH Keywords: Macdonald type integrals
zbMATH Keywords: cocharacters
zbMATH Keywords: codimensions
zbMATH Keywords: trace polynomial identities
zbMATH Keywords: matrix algebras
author: Amitai Regev
MaRDI profile type: Publication
full work available at URL: aima.1994.1055
OpenAlex ID: W2076803646
DOI: 10.1006/AIMA.1994.1055
description: scientific article; zbMATH DE number 638526