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Representation theorya combinatorial...

Prasad, Amritanshu.

Representation theorya combinatorial viewpoint /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Representation theoryAmritanshu Prasad.
其他題名:	a combinatorial viewpoint /
作者:	Prasad, Amritanshu.
出版者:	Cambridge :Cambridge University Press,2015.
面頁冊數:	xii, 191 p. :ill., digital ;24 cm.
標題:	Combinatorial group theory.
電子資源:	https://doi.org/10.1017/CBO9781139976824
ISBN:	9781139976824$q(electronic bk.)

Representation theorya combinatorial viewpoint /
Prasad, Amritanshu.

Representation theorya combinatorial viewpoint /[electronic resource] :Amritanshu Prasad. - Cambridge :Cambridge University Press,2015. - xii, 191 p. :ill., digital ;24 cm. - Cambridge studies in advanced mathematics ;147. - Cambridge studies in advanced mathematics ;105..

This book discusses the representation theory of symmetric groups, the theory of symmetric functions and the polynomial representation theory of general linear groups. The first chapter provides a detailed account of necessary representation-theoretic background. An important highlight of this book is an innovative treatment of the Robinson-Schensted-Knuth correspondence and its dual by extending Viennot's geometric ideas. Another unique feature is an exposition of the relationship between these correspondences, the representation theory of symmetric groups and alternating groups and the theory of symmetric functions. Schur algebras are introduced very naturally as algebras of distributions on general linear groups. The treatment of Schur-Weyl duality reveals the directness and simplicity of Schur's original treatment of the subject. In addition, each exercise is assigned a difficulty level to test readers' learning. Solutions and hints to most of the exercises are provided at the end.

ISBN: 9781139976824$q(electronic bk.)Subjects--Topical Terms:

190920
Combinatorial group theory.

LC Class. No.: QA182.5 / .P73 2015

Dewey Class. No.: 515.7223

Representation theorya combinatorial viewpoint /
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100 1 $a Prasad, Amritanshu. $3 709466
245 1 0 $a Representation theory $h [electronic resource] : $b a combinatorial viewpoint / $c Amritanshu Prasad.
260 $a Cambridge : $b Cambridge University Press, $c 2015.
300 $a xii, 191 p. : $b ill., digital ; $c 24 cm.
490 1 $a Cambridge studies in advanced mathematics ; $v 147
520 $a This book discusses the representation theory of symmetric groups, the theory of symmetric functions and the polynomial representation theory of general linear groups. The first chapter provides a detailed account of necessary representation-theoretic background. An important highlight of this book is an innovative treatment of the Robinson-Schensted-Knuth correspondence and its dual by extending Viennot's geometric ideas. Another unique feature is an exposition of the relationship between these correspondences, the representation theory of symmetric groups and alternating groups and the theory of symmetric functions. Schur algebras are introduced very naturally as algebras of distributions on general linear groups. The treatment of Schur-Weyl duality reveals the directness and simplicity of Schur's original treatment of the subject. In addition, each exercise is assigned a difficulty level to test readers' learning. Solutions and hints to most of the exercises are provided at the end.
650 0 $a Combinatorial group theory. $3 190920
650 0 $a Representations of groups. $3 191076
650 0 $a Symmetry groups. $3 185805
650 0 $a Symmetric functions. $3 245401
830 0 $a Cambridge studies in advanced mathematics ; $v 105. $3 541725
856 4 0 $u https://doi.org/10.1017/CBO9781139976824