2012/12/30 by Robert A. Proctor, Proctor, Robert A., Matthew J. Willis +1
Mathematics · #05E05 #05E10 #17B10 #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.1212.6789
openalex publication_date 2012/12/30 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28
The Schur function indexed by a partition lambda with at most n parts is the\nsum of the weight monomials for the Young tableaux of shape lambda. Let pi be\nan n-permutation. We give two descriptions of the tableaux that contribute\ntheir monomials to the key polynomial indexed by pi and lambda. (These\npolynomials are the characters of the Demazure modules for GL(n).) The "atom"\nindexed by pi is the sum of weight monomials of the tableaux whose right keys\nare the "key" tableau for pi. Schur functions and key polynomials can be\ndecomposed into sums of atoms. We also describe the tableaux that contribute to\nan atom, the tableaux that have a left key equal to a given key, and the\ntableaux that have a left key bounded below by a given key.\n