Catalan functions and $k$-Schur positivity
Combinatorics
2018-04-12 v1 Quantum Algebra
Abstract
We prove that graded -Schur functions are -equivariant Euler characteristics of vector bundles on the flag variety, settling a conjecture of Chen-Haiman. We expose a new miraculous shift invariance property of the graded -Schur functions and resolve the Schur positivity and -branching conjectures in the strongest possible terms by providing direct combinatorial formulas using strong marked tableaux.
Cite
@article{arxiv.1804.03701,
title = {Catalan functions and $k$-Schur positivity},
author = {Jonah Blasiak and Jennifer Morse and Anna Pun and Daniel Summers},
journal= {arXiv preprint arXiv:1804.03701},
year = {2018}
}
Comments
43 pages, 2 figures