- Unique rectification in d-complete posets
- Project Year:
2017
- REU Student (s):
Rahul Ilango | Rutgers University
| Michael Zlatin | Rutgers University
- Student 1 Institution:
Rutgers University-New Brunswick
- Student 2 Institution:
Rutgers University-New Brunswick
- Project Mentor:
Oliver Pechenik
- Project Mentor Area:
Mathematics
- Project Abstract:
Schubert calculus studies Schubert structure constants for the cohomology
rings of a homogeneous space X. In many cases, combinatorial rules involving
jeu de taquin on posets associated to these spaces have given positive formulas
for these constants. Schutzenberger first proved such a rule for X a Grassmanian.
Chaput and Perrin extended this to products of Λ-minuscule classes of spaces under
a Kac-Moody group. This includes all Schubert classes for X a minuscule variety.
Meanwhile, Buch, Samuel, Thomas, and Yong extended the jeu de taquin theory
to the K-theory of all minuscule varieties. We begin to develop the analogous
K-theoretic jeu de taquin theory for Proctor's d-complete posets, which are the
associated posets for Λ-minuscule Schubert varieties.
