Degree Type
Dissertation
Date of Award
1980
Degree Name
Doctor of Philosophy
Department
Mathematics
Abstract
Using a construction due to A. Young, H. Boerner gives a prescription for writing down the matrices for the natural (integral) irreducible representation of the symmetric group S(,n) H. Boerner, Representations of Groups with Special Consideration for the Needs of Modern Physics, North Holland Publishing Co., Amsterdam, 1963, p. 119. Writing down the matrices using this prescription is rather tedious, and becomes computationally impossible for large n (n (GREATERTHEQ) 10) because of the need to calculate chains;This dissertation greatly simplifies the computation of the matrices for the natural (integral) irreducible representation of the symmetric group S(,n) by eliminating the need to calculate chains. The calculation of the chains is replaced by the simple act of setting up and inverting an upper triangular matrix, A(I). In many cases a set of tableaux which is not necessarily standard can be chosen so that A(I) is the identity matrix. Such a set of tableaux is called a complete set of orthogonal tableaux, and yields an equivalent representation of S(,n) in which all entries of the matrices are +1, -1, or 0.
DOI
https://doi.org/10.31274/rtd-180813-11435
Publisher
Digital Repository @ Iowa State University, http://lib.dr.iastate.edu/
Copyright Owner
Joseph Milton Clifton
Copyright Date
1980
Language
en
Proquest ID
AAI8103436
File Format
application/pdf
File Size
86 pages
Recommended Citation
Clifton, Joseph Milton, "Complete sets of orthogonal tableaux " (1980). Retrospective Theses and Dissertations. 6689.
https://lib.dr.iastate.edu/rtd/6689
