Catalan functions and k-Schur positivity

2018/04/10 by Blasiak, Jonah, Morse, Jennifer, Pun, Anna +1 · 2 citations
#14N15 #33D52 #Combinatorics (math.CO) #FOS: Mathematics #Primary: 05E05 #Quantum Algebra (math.QA) #Secondary: 05A30

paper · doi:10.48550/arxiv.1804.03701

Abstract

We prove that graded k-Schur functions are G-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 k-Schur functions and resolve the Schur positivity and k-branching conjectures in the strongest possible terms by providing direct combinatorial formulas using strong marked tableaux.

Cited by

• The nonsymmetric shuffle theorem
• Weighted K-k-Schur functions and their application to the K-k-Schur alternating conjecture

Related

• K-theoretic Catalan functions
• Demazure crystals and the Schur positivity of Catalan functions
• k-Schur expansions of Catalan functions
• Categorification of k-Schur functions and refined Macdonald positivity
• A geometric realization of Catalan functions