Skip to main content
We gratefully acknowledge support from the Simons Foundation, member institutions, and all contributors. Donate
arXiv logo
Cornell University Logo

Mathematics > Algebraic Geometry

arXiv:1807.10784 (math)
[Submitted on 27 Jul 2018 (v1), last revised 15 Apr 2020 (this version, v2)]

Title:Theta and eta polynomials in geometry, Lie theory, and combinatorics

Authors:Harry Tamvakis
View PDF
Abstract:The classical Schur polynomials form a natural basis for the ring of symmetric polynomials, and have geometric significance since they represent the Schubert classes in the cohomology ring of Grassmannians. Moreover, these polynomials enjoy rich combinatorial properties. In the last decade, an exact analogue of this picture has emerged in the symplectic and orthogonal Lie types, with the Schur polynomials replaced by the theta and eta polynomials of Buch, Kresch, and the author. This expository paper gives an overview of what is known to date about this correspondence, with examples.
Comments: 35 pages, 6 figures, final version. Published in "First Congress of Greek Mathematicians", Proceedings of the Congress held in Athens, Greece, June 25-30, 2018
Subjects: Algebraic Geometry (math.AG); Combinatorics (math.CO); Representation Theory (math.RT)
MSC classes: 14M15, 05E05, 14M17, 14N15, 05E15
Cite as: arXiv:1807.10784 [math.AG]
  (or arXiv:1807.10784v2 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.1807.10784

Submission history

From: Harry Tamvakis [view email]
[v1] Fri, 27 Jul 2018 18:34:17 UTC (41 KB)
[v2] Wed, 15 Apr 2020 01:00:08 UTC (41 KB)
Full-text links:

Access Paper:

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

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?)