Topics in computational algebra
著者
書誌事項
Topics in computational algebra
Kluwer, c1990
- : alk. paper
大学図書館所蔵 全20件
  青森
  岩手
  宮城
  秋田
  山形
  福島
  茨城
  栃木
  群馬
  埼玉
  千葉
  東京
  神奈川
  新潟
  富山
  石川
  福井
  山梨
  長野
  岐阜
  静岡
  愛知
  三重
  滋賀
  京都
  大阪
  兵庫
  奈良
  和歌山
  鳥取
  島根
  岡山
  広島
  山口
  徳島
  香川
  愛媛
  高知
  福岡
  佐賀
  長崎
  熊本
  大分
  宮崎
  鹿児島
  沖縄
  韓国
  中国
  タイ
  イギリス
  ドイツ
  スイス
  フランス
  ベルギー
  オランダ
  スウェーデン
  ノルウェー
  アメリカ
注記
Papers presented at the Semester in Computational Algebra, held at the University of Rome "Tor Vergata," spring 1990
"Reprinted from Acta applicandae mathematicae, volume 21, nos. 1 & 2 (1990)."
Includes bibliographical references
内容説明・目次
内容説明
The main purpose of these lectures is first to briefly survey the fundamental con nection between the representation theory of the symmetric group Sn and the theory of symmetric functions and second to show how combinatorial methods that arise naturally in the theory of symmetric functions lead to efficient algorithms to express various prod ucts of representations of Sn in terms of sums of irreducible representations. That is, there is a basic isometry which maps the center of the group algebra of Sn, Z(Sn), to the space of homogeneous symmetric functions of degree n, An. This basic isometry is known as the Frobenius map, F. The Frobenius map allows us to reduce calculations involving characters of the symmetric group to calculations involving Schur functions. Now there is a very rich and beautiful theory of the combinatorics of symmetric functions that has been developed in recent years. The combinatorics of symmetric functions, then leads to a number of very efficient algorithms for expanding various products of Schur functions into a sum of Schur functions. Such expansions of products of Schur functions correspond via the Frobenius map to decomposing various products of irreducible representations of Sn into their irreducible components. In addition, the Schur functions are also the characters of the irreducible polynomial representations of the general linear group over the complex numbers GLn(C).
目次
Branching Functions for Winding Subalgebras and Tensor Products.- Computing with Characters of Finite Groups.- Some Remarks on the Computation of Complements and Normalizers in Soluble Groups.- Methods for Computing in Algebraic Geometry and Commutative Algebra.- Combinatorial Algorithms for the Expansion of Various Products of Schur Functions.- Polynomial Identities for 2 x 2 Matrices.- Cayley Factorization and a Straightening Algorithm.- The Nagata-Higman Theorem.- Supersymmetric Bracket Algebra and Invariant Theory.- Aspects of Characteristic-Free Representation Theory of GLn, and Some Applications to Intertwining Numbers.
「Nielsen BookData」 より