Skip to main content
We gratefully acknowledge support from the Simons Foundation, member institutions, and all contributors. Donate
arXiv logo
Cornell University Logo

Mathematics > Representation Theory

arXiv:1810.02948 (math)
[Submitted on 6 Oct 2018 (v1), last revised 31 Mar 2019 (this version, v2)]

Title:Ringel duals of Brauer algebras via super groups

Authors:Kevin Coulembier
View PDF
Abstract:We prove that the Brauer algebra, for all parameters for which it is quasi-hereditary, is Ringel dual to a category of representations of the orthosymplectic super group. As a consequence we obtain new and algebraic proofs for some results on the fundamental theorems of invariant theory for this super group over the complex numbers and also extend them to some cases in positive characteristic. Our methods also apply to the walled Brauer algebra in which case we obtain a duality with the general linear super group, with similar applications.
Comments: v2: simplified and shorter Section 3
Subjects: Representation Theory (math.RT)
Cite as: arXiv:1810.02948 [math.RT]
  (or arXiv:1810.02948v2 [math.RT] for this version)
  https://doi.org/10.48550/arXiv.1810.02948

Submission history

From: Kevin Coulembier [view email]
[v1] Sat, 6 Oct 2018 07:37:32 UTC (24 KB)
[v2] Sun, 31 Mar 2019 23:52:19 UTC (23 KB)
Full-text links:

Access Paper:

view license
Current browse context:
math.RT
< prev   |   next >
new | recent | 2018-10
Change to browse by:
math

References & Citations

export BibTeX citation

Bookmark

BibSonomy logo Reddit logo

Bibliographic and Citation Tools

Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)

Code, Data and Media Associated with this Article

alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)

Demos

Replicate (What is Replicate?)
Hugging Face Spaces (What is Spaces?)
TXYZ.AI (What is TXYZ.AI?)

Recommenders and Search Tools

Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)