Skip to main content

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
Cancel
×
×
Home
  • Home
Article
  • Access

Multiplicity-free quotient tensor algebras

  • G. E. Wall (a1)
Abstract

Let V be an infinite-dimensional vector space ovre a field of characteristic 0. It is well known that the tensor algebra T on V is a completely reducible module for the general linear group G on V. This paper is concerned with those quotient algebras A of T that are at the same time modules for G. A partial solution is given to the problem of determinig those A in which no irreducible constitutent has multiplicity greater thatn 1.

    •
      • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Multiplicity-free quotient tensor algebras
      Available formats
      ×
      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      Multiplicity-free quotient tensor algebras
      Available formats
      ×
      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      Multiplicity-free quotient tensor algebras
      Available formats
      ×
Copyright
COPYRIGHT: © Australian Mathematical Society 2001
References
Hide All
[1]Dixmier, J., Enveloping algebras (North-Holland, Amsterdam, 1977).
[2]Inglis, N. F. J., Richardson, R. W. and Saxl, J., ‘An explicit model for the complex representations of Sn’, Arch. Math. 54 (1990), 258–259.
[3]Kljačko, A. A., ‘Models for complex representations of the groups GL(n, q) adn Weyl groups’, Soviet Math. Doklady 24 (1981), 496–499.
[4]Macdonald, I. G., Symmetric functions and Hall polynomials, 2nd edition (Oxford University Press, Oxford, 1994).
[5]Wall, G. E., ‘A note on multiplicity-free tensor representations’, J. Pure Appl. Algebra 88 (1993), 249–263.
[6]Wall, G. E., ‘More on multiplicty-free tensor representations’, Research report 95–29, (School of Mathematics and Statistics, University of Sydney, 1995).
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of the Australian Mathematical Society
  • ISSN: 1446-7887
  • EISSN: 1446-8107
  • URL: /core/journals/journal-of-the-australian-mathematical-society
Please enter your name
Please enter a valid email address
Who would you like to send this to? *

CAPTCHA *

Skip to the audio challenge
×
MathJax

Keywords:

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 20 *
Loading metrics...

Abstract views

Total abstract views: 39 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 13th June 2018. This data will be updated every 24 hours.

Cancel
Confirm
×