Article Navigation
- < Previous
- Next >
Journal Article
Get access
Calder Morton-Ferguson Massachusetts Institute of Technology , 77 Massachusetts Ave., Cambridge, MA 02141, USA Correspondence to be sent to: e-mail: caldermf@mit.edu Search for other works by this author on: Oxford Academic
International Mathematics Research Notices, Volume 2024, Issue 13, July 2024, Pages 10219–10235, https://doi.org/10.1093/imrn/rnae052
Published:
11 April 2024
Article history
Received:
02 April 2023
Revision received:
25 November 2023
Accepted:
25 November 2023
Published:
11 April 2024
- Views
- Article contents
- Figures & tables
- Video
- Audio
- Supplementary Data
-
Cite
Cite
Calder Morton-Ferguson, Symplectic Fourier–Deligne Transforms on G/U and the Algebra of Braids and Ties, International Mathematics Research Notices, Volume 2024, Issue 13, July 2024, Pages 10219–10235, https://doi.org/10.1093/imrn/rnae052
Close
Search
Close
Search
Advanced Search
Search Menu
Abstract
We explicitly identify the algebra generated by symplectic Fourier–Deligne transforms (i.e., convolution with Kazhdan–Laumon sheaves) acting on the Grothendieck group of perverse sheaves on the basic affine space |$G/U$|, answering a question originally raised by A. Polishchuk. We show it is isomorphic to a distinguished subalgebra, studied by I. Marin, of the generalized algebra of braids and ties (defined in Type |$A$| by F. Aicardi and J. Juyumaya and generalized to all types by Marin), providing a connection between geometric representation theory and an algebra defined in the context of knot theory. Our geometric interpretation of this algebra entails some algebraic consequences: we obtain a short and type-independent geometric proof of the braid relations for Juyumaya’s generators of the Yokonuma–Hecke algebra (previously proved case-by-case in types |$A, D, E$| by Juyumaya and separately for types |$B, C, F_{4}, G_{2}$| by Juyumaya and S. S. Kannan), a natural candidate for an analogue of a Kazhdan–Lusztig basis, and finally an explicit formula for the dimension of Marin’s algebra in Type |$A_{n}$| (previously only known for |$n \leq 4$|).
© The Author(s) 2024. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permission@oup.com.
This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (https://academic.oup.com/pages/standard-publication-reuse-rights)
Issue Section:
Article
You do not currently have access to this article.
Download all slides
Sign in
Get help with access
Personal account
- Sign in with email/username & password
- Get email alerts
- Save searches
- Purchase content
- Activate your purchase/trial code
- Add your ORCID iD
Sign in Register
Institutional access
- Sign in with a library card
- Sign in with username/password
- Recommend to your librarian
Sign in through your institution
Sign in through your institution
Institutional account management
Sign in as administrator
Get help with access
Institutional access
Access to content on Oxford Academic is often provided through institutional subscriptions and purchases. If you are a member of an institution with an active account, you may be able to access content in one of the following ways:
IP based access
Typically, access is provided across an institutional network to a range of IP addresses. This authentication occurs automatically, and it is not possible to sign out of an IP authenticated account.
Sign in through your institution
Choose this option to get remote access when outside your institution. Shibboleth/Open Athens technology is used to provide single sign-on between your institution’s website and Oxford Academic.
- Click Sign in through your institution.
- Select your institution from the list provided, which will take you to your institution's website to sign in.
- When on the institution site, please use the credentials provided by your institution. Do not use an Oxford Academic personal account.
- Following successful sign in, you will be returned to Oxford Academic.
If your institution is not listed or you cannot sign in to your institution’s website, please contact your librarian or administrator.
Sign in with a library card
Enter your library card number to sign in. If you cannot sign in, please contact your librarian.
Society Members
Society member access to a journal is achieved in one of the following ways:
Sign in through society site
Many societies offer single sign-on between the society website and Oxford Academic. If you see ‘Sign in through society site’ in the sign in pane within a journal:
- Click Sign in through society site.
- When on the society site, please use the credentials provided by that society. Do not use an Oxford Academic personal account.
- Following successful sign in, you will be returned to Oxford Academic.
If you do not have a society account or have forgotten your username or password, please contact your society.
Sign in using a personal account
Some societies use Oxford Academic personal accounts to provide access to their members. See below.
Personal account
A personal account can be used to get email alerts, save searches, purchase content, and activate subscriptions.
Some societies use Oxford Academic personal accounts to provide access to their members.
Viewing your signed in accounts
Click the account icon in the top right to:
- View your signed in personal account and access account management features.
- View the institutional accounts that are providing access.
Signed in but can't access content
Oxford Academic is home to a wide variety of products. The institutional subscription may not cover the content that you are trying to access. If you believe you should have access to that content, please contact your librarian.
Institutional account management
For librarians and administrators, your personal account also provides access to institutional account management. Here you will find options to view and activate subscriptions, manage institutional settings and access options, access usage statistics, and more.
Purchase
Subscription prices and ordering for this journal
Purchasing options for books and journals across Oxford Academic
Short-term Access
To purchase short-term access, please sign in to your personal account above.
Don't already have a personal account? Register
Symplectic Fourier–Deligne Transforms on G/U and the Algebra of Braids and Ties - 24 Hours access
EUR €16.00
GBP £14.00
USD $17.00
Rental
This article is also available for rental through DeepDyve.
Advertisem*nt
Citations
Views
111
Altmetric
More metrics information
Metrics
Total Views 111
77 Pageviews
34 PDF Downloads
Since 4/1/2024
| Month: | Total Views: |
|---|---|
| April 2024 | 44 |
| May 2024 | 34 |
| June 2024 | 10 |
| July 2024 | 23 |
Citations
Powered by Dimensions
Altmetrics
Email alerts
Article activity alert
Advance article alerts
New issue alert
Receive exclusive offers and updates from Oxford Academic
Citing articles via
Google Scholar
-
Latest
-
Most Read
-
Most Cited
More from Oxford Academic
Mathematics
Pure Mathematics
Science and Mathematics
Books
Journals
Advertisem*nt
