Representation Theory of Symmetric Groups (Discrete Mathematics and Its Applications)
暫譯: 對稱群的表示理論(離散數學及其應用)
Pierre-Loic Meliot
- 出版商: Chapman and Hall/CRC
- 出版日期: 2017-03-21
- 售價: $8,420
- 貴賓價: 9.5 折 $7,999
- 語言: 英文
- 頁數: 682
- 裝訂: Hardcover
- ISBN: 1498719120
- ISBN-13: 9781498719124
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商品描述
Representation Theory of Symmetric Groups is the most up-to-date abstract algebra book on the subject of symmetric groups and representation theory. Utilizing new research and results, this book can be studied from a combinatorial, algorithmic or algebraic viewpoint.
This book is an excellent way of introducing today’s students to representation theory of the symmetric groups, namely classical theory. From there, the book explains how the theory can be extended to other related combinatorial algebras like the Iwahori-Hecke algebra.
In a clear and concise manner, the author presents the case that most calculations on symmetric group can be performed by utilizing appropriate algebras of functions. Thus, the book explains how some Hopf algebras (symmetric functions and generalizations) can be used to encode most of the combinatorial properties of the representations of symmetric groups.
Overall, the book is an innovative introduction to representation theory of symmetric groups for graduate students and researchers seeking new ways of thought.
商品描述(中文翻譯)
《對稱群的表示理論》是關於對稱群和表示理論的最新抽象代數書籍。利用最新的研究和結果,本書可以從組合、算法或代數的角度進行學習。
這本書是向當今學生介紹對稱群的表示理論(即古典理論)的絕佳方式。接著,書中解釋了如何將該理論擴展到其他相關的組合代數,例如 Iwahori-Hecke 代數。
作者以清晰簡潔的方式提出,大多數對稱群的計算可以通過利用適當的函數代數來進行。因此,本書解釋了某些 Hopf 代數(對稱函數及其推廣)如何用來編碼對稱群表示的大多數組合性質。
總體而言,本書是對於研究生和尋求新思維的研究人員來說,對稱群表示理論的創新介紹。