Catalan functions and $k$-Schur positivity
JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY(2019)
摘要
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.
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关键词
k-Schur functions,Schur positivity,branching rule,spin,strong tableaux,generalized Kostka polynomials
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