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:1812.08546 (math)
[Submitted on 20 Dec 2018 (v1), last revised 14 May 2019 (this version, v3)]

Title:On the number of constituents of induced modules of Ariki-Koike algebras

Authors:Christoph Schoennenbeck
View PDF
Abstract:We examine the crystal graph of the $\widehat{\mathfrak{sl}}_e$-module arising from an $\widehat{\mathfrak{sl}}_e$-categorification to study the defining endo-functors of the categorification. This yields lower bounds on the number of irreducible constituents of certain objects. We use Ariki's categorification result on Ariki-Koike algebras to obtain a new lower bound on the number of constituents of their parabolically induced modules. In particular this will imply reducibility of every induced module.
Comments: v3:20 pages, worked in comments by reviewer, extended proofs
Subjects: Representation Theory (math.RT)
MSC classes: 05E10, 20C08, 17B10
Cite as: arXiv:1812.08546 [math.RT]
  (or arXiv:1812.08546v3 [math.RT] for this version)
  https://doi.org/10.48550/arXiv.1812.08546

Submission history

From: Christoph Schoennenbeck [view email]
[v1] Thu, 20 Dec 2018 13:19:34 UTC (22 KB)
[v2] Thu, 3 Jan 2019 09:24:23 UTC (24 KB)
[v3] Tue, 14 May 2019 11:00:29 UTC (25 KB)
Full-text links:

Access Paper:

  • View PDF
  • TeX Source
  • Other Formats
view license
Current browse context:
math.RT
< prev   |   next >
new | recent | 2018-12
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?)