This thesis considers symmetric functions and algebraic combinatorics via the polynomial representation theory of GL(N,C). In particular, we utilise the theory of Jacobi-Trudi determinants to prove some new results pertaining to the Littlewood-Richardson coefficients. Our results imply, under some hypotheses on the strictness of the partition an equality between Littlewood-Richardson coefficients and Kostka numbers. For the case that a suitable partition has two rows, an explicit formula is then obtained for the Littlewood-Richardson coefficient using the Hook Length formula. All these results are then applied to compute branching laws for GL(m+n,C) restricting to GL(m,C) x GL(n,C). The technique also implies the well-known Racah formula.
| Identifer | oai:union.ndltd.org:ADTP/242980 |
| Date | January 2007 |
| Creators | Hall, Jack Kingsbury, Mathematics & Statistics, Faculty of Science, UNSW |
| Publisher | Awarded by:University of New South Wales. Mathematics and Statistics |
| Source Sets | Australiasian Digital Theses Program |
| Language | English |
| Detected Language | English |
| Rights | Copyright Jack Kingsbury Hall, http://unsworks.unsw.edu.au/copyright |
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