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
×
Home
  • Home
EnglishFrançais
Proceedings of the London Mathematical Society Proceedings of the London Mathematical Society

Article contents

Representations of Ariki–Koike algebras and Gröbner–Shirshov bases

Published online by Cambridge University Press:  30 June 2004

Seok-Jin Kang ,
In-Sok Lee ,
Kyu-Hwan Lee  and
Hyekyung Oh
Seok-Jin Kang
Affiliation:
School of Mathematics, Korea Institute for Advanced Study, 207-43 Cheongryangri-Dong, Dongdaemun-Gu, Seoul 130-722, Korea. E-mail: sjkang@kias.re.kr
In-Sok Lee
Affiliation:
Department of Mathematics, Seoul National University, Seoul 151-747, Korea. E-mail: islee@math.snu.ac.kr
Kyu-Hwan Lee
Affiliation:
Department of Mathematics, University of Toronto, Toronto, ON M5S 3G3, Canada. E-mail: khlee@math.toronto.edu
Hyekyung Oh
Affiliation:
Department of Mathematics, Seoul National University, Seoul 151-747, Korea. E-mail: hyekyung@math.snu.ac.kr
Get access

Abstract

In this paper, we investigate the structure of Ariki–Koike algebras and their Specht modules using Gröbner–Shirshov basis theory and combinatorics of Young tableaux. For a multipartition $\lambda$, we find a presentation of the Specht module $S^{\lambda}$ given by generators and relations, and determine its Gröbner–Shirshov pair. As a consequence, we obtain a linear basis of $S^{\lambda}$ consisting of standard monomials with respect to the Gröbner–Shirshov pair. We show that this monomial basis can be canonically identified with the set of cozy tableaux of shape $\lambda$.

Keywords

Ariki–Koike algebras Specht modules Gröbner–Shirshov basis tableaux 16Gxx 05Exx
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 89 , Issue 1 , July 2004 , pp. 54 - 70
Copyright
2004 London Mathematical Society

Access options

Get access to the full version of this content by using one of the access options below.
If you should have access and can't see this content please contact technical support.

Footnotes

The research of the first author was supported by KOSEF Grant # 98-0701-01-5-L and the Young Scientist Award, Korean Academy of Science and Technology.
The research of the other three authors was supported by KOSEF Grant # 98-0701-01-5-L and BK21 Mathematical Sciences Division, Seoul National University.

Full text views

Full text views reflects PDF downloads, PDFs sent to Google Drive, Dropbox and Kindle and HTML full text views.

Total number of HTML views: 0
Total number of PDF views: 5 *
View data table for this chart

* Views captured on Cambridge Core between September 2016 - 25th January 2021. This data will be updated every 24 hours.

9 Cited by
Hostname: page-component-898fc554b-sztd2 Total loading time: 0.251 Render date: 2021-01-25T15:10:53.980Z Query parameters: { "hasAccess": "0", "openAccess": "0", "isLogged": "0", "lang": "en" } Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": false, "newCiteModal": false }

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.

Representations of Ariki–Koike algebras and Gröbner–Shirshov bases
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.

Representations of Ariki–Koike algebras and Gröbner–Shirshov bases
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.

Representations of Ariki–Koike algebras and Gröbner–Shirshov bases
Available formats
×
×

Reply to: Submit a response

Your details

Conflicting interests

Do you have any conflicting interests? *