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/0010089 (math)
[Submitted on 10 Oct 2000 (v1), last revised 31 Dec 2011 (this version, v2)]

Title:On tensor categories attached to cells in affine Weyl groups

Authors:Roman Bezrukavnikov
View PDF
Abstract:We prove a conjecture by Lusztig, which describes the tensor categories of perverse sheaves on affine flag manifolds, with tensor structure provided by truncated convolution, in terms of the Langlands dual group. We also give a geometric (categorical) description of Lusztig's bijection between two-sided cells in an affine Weyl group, and unipotent conjugacy classes in the Langlands dual group. The main tool is the sheaf-theoretic construction of the center of the affine Hecke algebra due to Gaitsgory (based on ideas of Beilinson and Kottwitz), see math.AG/9912074.
Comments: The published version of this paper misquoted a result of Lusztig, this version corrects this mistake (thanks to Xinwen Zhu for pointing it out)
Subjects: Representation Theory (math.RT); Category Theory (math.CT)
Cite as: arXiv:math/0010089 [math.RT]
  (or arXiv:math/0010089v2 [math.RT] for this version)
  https://doi.org/10.48550/arXiv.math/0010089
Journal reference: in: "Representation theory of algebraic groups and quantum groups," 69--90, Adv. Stud. Pure Math., 40, Math. Soc. Japan, Tokyo, 2004

Submission history

From: Roman Bezrukavnikov [view email]
[v1] Tue, 10 Oct 2000 20:37:15 UTC (25 KB)
[v2] Sat, 31 Dec 2011 13:58:21 UTC (25 KB)
Full-text links:

Access Paper:

view license
Current browse context:
math.RT
< prev   |   next >
new | recent | 2000-10

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?)