Identities Relating Schur s-Functions and Q-Functions.

Symmetric Functions;Schur Functions;Q-functions;S-functions;Tableaux;Shifted Tableaux;Mathematics;Science;Mathematics

DeWitt, Elizabeth AngelaBlass, Andreas R. ;

University of Michigan

关键词: Symmetric Functions;    Schur Functions;    Q-functions;    S-functions;    Tableaux;    Shifted Tableaux;    Mathematics;    Science;    Mathematics;   

Others  :  https://deepblue.lib.umich.edu/bitstream/handle/2027.42/93841/edewitt_1.pdf?sequence=1&isAllowed=y

瑞士|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

Schur s- and Q-functions are two important families of symmetric functions, withapplications for other fields, such as the representation theory of the symmetricgroup. Other researchers have shown that there are unexpected equalities betweenseemingly unrelated skew s-functions. In this dissertation we investigate similarrelationships among Q-functions and between s- and Q-functions. In particular,we determine which s-functions are a linear combination of Q-functions, showingin addition that all are Q-positive, and determine which s-functions are constantmultiples of single non-skew Q-functions. For skew Q-functions whose diagrams arevalid unshifted shapes, we determine which ones are constant multiples of singlenon-skew Q-functions.