2025/05/29 by Kato, Syu
#05E05 #20G05 #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.2505.23202
We characterize the k-Schur functions as the graded characters of simple objects in an additive module category. This confirms a set of conjectures formulated in the Ph.D. thesis of Chen, written under the direction of Mark Haiman, and thereby establishes the algebraic framework proposed therein. As a consequence, we deduce that the modified Macdonald polynomials are k-Schur positive, thus realizing the original motivation behind the definition of the k-Schur functions by Lapointe, Lascoux, and Morse. Our approach builds on our previous work on the algebraic and geometric realization of Catalan symmetric functions, which encompasses both the k-Schur functions and the Hall--Littlewood functions.