Catalan functions and $k$-Schur positivity

Autor:	Blasiak, Jonah, Morse, Jennifer, Pun, Anna, Summers, Daniel
Rok vydání:	2018
Předmět:	Mathematics - Combinatorics Mathematics - Quantum Algebra Primary: 05E05 14N15 Secondary: 05A30 33D52
Druh dokumentu:	Working Paper
Popis:	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. Comment: 43 pages, 2 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1804.03701 Zobrazit plný text záznamu View this record from Arxiv