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:1807.02179 (math)
[Submitted on 5 Jul 2018 (v1), last revised 4 Mar 2019 (this version, v3)]

Title:Interpolating factorizations for acyclic Donaldson--Thomas invariants

Authors:Justin Allman
View PDF
Abstract:We prove a family of factorization formulas for the combinatorial Donaldson--Thomas invariant for an acyclic quiver. A quantum dilogarithm identity due to Reineke, later interpreted by Rimanyi by counting codimensions of quiver loci, gives two extremal cases of our formulation in the Dynkin case. We establish our interpolating factorizations explicitly with a dimension counting argument by defining certain stratifications of the space of representations for the quiver and calculating Betti numbers in the corresponding equivariant cohomology algebras.
Comments: several expositional edits; 21 pages
Subjects: Representation Theory (math.RT); Algebraic Geometry (math.AG); Algebraic Topology (math.AT)
MSC classes: Primary 16G20, Secondary 05E10, 05E15, 55N91, 55T99
Cite as: arXiv:1807.02179 [math.RT]
  (or arXiv:1807.02179v3 [math.RT] for this version)
  https://doi.org/10.48550/arXiv.1807.02179

Submission history

From: Justin Allman [view email]
[v1] Thu, 5 Jul 2018 20:57:44 UTC (23 KB)
[v2] Sun, 15 Jul 2018 20:03:52 UTC (23 KB)
[v3] Mon, 4 Mar 2019 15:46:45 UTC (24 KB)
Full-text links:

Access Paper:

view license
Current browse context:
math.RT
< prev   |   next >
new | recent | 2018-07
Change to browse by:
math
math.AG
math.AT

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?)