Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
  1. Home
  2. Books
  3. Combinatorics of Minuscule Representations
  • Cited by 18
Publisher:
Cambridge University Press
Online publication date:
February 2013
Print publication year:
2013
Online ISBN:
9781139207003
DOI:
https://doi.org/10.1017/CBO9781139207003
Subjects:
Mathematics (general), Mathematics, Algebra
Series:
Cambridge Tracts in Mathematics (199)
Information

Book description

Minuscule representations occur in a variety of contexts in mathematics and physics. They are typically much easier to understand than representations in general, which means they give rise to relatively easy constructions of algebraic objects such as Lie algebras and Weyl groups. This book describes a combinatorial approach to minuscule representations of Lie algebras using the theory of heaps, which for most practical purposes can be thought of as certain labelled partially ordered sets. This leads to uniform constructions of (most) simple Lie algebras over the complex numbers and their associated Weyl groups, and provides a common framework for various applications. The topics studied include Chevalley bases, permutation groups, weight polytopes and finite geometries. Ideal as a reference, this book is also suitable for students with a background in linear and abstract algebra and topology. Each chapter concludes with historical notes, references to the literature and suggestions for further reading.

Reviews

'This monograph could be read with profit not only by the specialist, but also by an interested graduate student with some background on Lie algebras.'

Felipe Zaldivar Source: MAA Reviews

'The exposition [is] very clear. The book is strongly recommended to students and researchers who are interested in combinatorial aspects of representation theory.'

Hiro-Fumi Yamada Source: Mathematical Reviews

'… useful as a book for students, the book under review is particularly useful as a reference for researchers of relevant fields.'

Qendrim R. Gashi Source: Zentralblatt MATH

Refine List

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Save to Kindle
  • Save to Dropbox
  • Save to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
Cancel
×

Contents

Contents

Metrics

Altmetric attention score

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Book summary page views

Total views: 0 *
Loading metrics...

* Views captured on Cambridge Core between #date#. This data will be updated every 24 hours.

Usage data cannot currently be displayed.