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:1805.03109 (math)
[Submitted on 8 May 2018 (v1), last revised 10 May 2018 (this version, v2)]

Title:On the SO(n+3) to SO(n) branching multiplicity space

Authors:Emilio A. Lauret, Fiorela Rossi Bertone
View PDF
Abstract:We study the decomposition as an $\textrm{SO}(3)$-module of the multiplicity space corresponding to the branching from $\textrm{SO}(n+3)$ to $\textrm{SO}(n)$. Here, $\textrm{SO}(n)$ (resp.\ $\textrm{SO}(3)$) is considered embedded in $\textrm{SO}(n+3)$ in the upper left-hand block (resp.\ lower right-hand block). We show that when the highest weight of the irreducible representation of $\textrm{SO}(n)$ interlaces the highest weight of the irreducible representation of $\textrm{SO}(n+3)$, then the multiplicity space decomposes as a tensor product of $\lfloor (n+2)/2\rfloor$ reducible representations of $\textrm{SO}(3)$.
Subjects: Representation Theory (math.RT)
MSC classes: 20G05, 22E46
Cite as: arXiv:1805.03109 [math.RT]
  (or arXiv:1805.03109v2 [math.RT] for this version)
  https://doi.org/10.48550/arXiv.1805.03109
Journal reference: Comptes Rendus Acad. Sci. Paris, Ser. I Math. 356 (2018), 1112-1124
Related DOI: https://doi.org/10.1016/j.crma.2018.09.004

Submission history

From: Emilio Lauret [view email]
[v1] Tue, 8 May 2018 15:32:09 UTC (17 KB)
[v2] Thu, 10 May 2018 13:50:56 UTC (17 KB)
Full-text links:

Access Paper:

  • View PDF
  • TeX Source
  • Other Formats
view license
Current browse context:
math.RT
< prev   |   next >
new | recent | 2018-05
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?)