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:math/0702272 (math)
[Submitted on 9 Feb 2007 (v1), last revised 30 Jul 2007 (this version, v5)]

Title:On the determination of Kazhdan-Lusztig cells in affine Weyl groups with unequal parameters

Authors:Jeremie Guilhot
View PDF
Abstract: Let W be a Coxeter group and L be a weight function on W. Following Lusztig, we have a corresponding decomposition of W into left cells, which have important applications in representation theory. We study the case where $W$ is an affine Weyl group of type $\tilde{G_{2}}$. Using explicit computation with \textsf{CHEVIE}, we show that (1) there are only finitely many possible decompositions into left cells and (2) the number of left cells is finite in each case, thus confirming some of Lusztig's conjectures in this case. For the proof, we show some equalities on the Kazhdan-Lusztig polynomials which hold for any affine Weyl groups.
Comments: 22 pages, 2 figures, the revised version contains additional reference and some rewritting. Submitted
Subjects: Representation Theory (math.RT); Rings and Algebras (math.RA)
Cite as: arXiv:math/0702272 [math.RT]
  (or arXiv:math/0702272v5 [math.RT] for this version)
  https://doi.org/10.48550/arXiv.math/0702272

Submission history

From: Jeremie Guilhot [view email]
[v1] Fri, 9 Feb 2007 17:57:08 UTC (18 KB)
[v2] Mon, 12 Feb 2007 11:09:33 UTC (18 KB)
[v3] Thu, 15 Feb 2007 13:37:49 UTC (18 KB)
[v4] Tue, 20 Mar 2007 11:06:02 UTC (18 KB)
[v5] Mon, 30 Jul 2007 19:47:49 UTC (20 KB)
Full-text links:

Access Paper:

  • View PDF
  • TeX Source
  • Other Formats
view license
Current browse context:
math.RT
< prev   |   next >
new | recent | 2007-02

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?)