Group representation base vector expansions (for representations of S characterized by single-hook or by two-rowed Young tableaux)
Group representation base vector expansions (for representations of S characterized by single-hook or by two-rowed Young tableaux)
In this thesis the base vectors for irreducible representations of the sy_tetric group n, for the two particular cases(a) Representations characterized by the partition [n-k.1 kI - so called single-hook representations;.(b) Representations characterized by the partition Cn-m,m] - so called double-row representations,are given explicitly as linear combinations of determinantal functions.Chapters I, II and III with the corresponding Tables I, II and III. give expansions for the base vectors of [n-k.1kI Chapter I has type I expansions with (k+1)-rowed determinants having k variables. Chapter II describes type II, expansions in terms of k-rowed determinants with k variables. Chapter III has type III expansions with %k+1) -rowed determinants with k+1 variables, described however in terms of the states missing from the determinants. Chapter IV gives a very simple expansion of the base vectors for Cn-m,m] in terms of m-fold products of type I two-rowed determinants with one variable.'A1Z Tables go- up to the value n=10. The Introduction brings detailed examples illustrating the various types of expansion.
University of Southampton
El-Sharkaway, Nahid Gamal Ibrahim
1975
El-Sharkaway, Nahid Gamal Ibrahim
El-Sharkaway, Nahid Gamal Ibrahim
(1975)
Group representation base vector expansions (for representations of S characterized by single-hook or by two-rowed Young tableaux).
University of Southampton, Doctoral Thesis.
Record type:
Thesis
(Doctoral)
Abstract
In this thesis the base vectors for irreducible representations of the sy_tetric group n, for the two particular cases(a) Representations characterized by the partition [n-k.1 kI - so called single-hook representations;.(b) Representations characterized by the partition Cn-m,m] - so called double-row representations,are given explicitly as linear combinations of determinantal functions.Chapters I, II and III with the corresponding Tables I, II and III. give expansions for the base vectors of [n-k.1kI Chapter I has type I expansions with (k+1)-rowed determinants having k variables. Chapter II describes type II, expansions in terms of k-rowed determinants with k variables. Chapter III has type III expansions with %k+1) -rowed determinants with k+1 variables, described however in terms of the states missing from the determinants. Chapter IV gives a very simple expansion of the base vectors for Cn-m,m] in terms of m-fold products of type I two-rowed determinants with one variable.'A1Z Tables go- up to the value n=10. The Introduction brings detailed examples illustrating the various types of expansion.
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Published date: 1975
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Local EPrints ID: 462354
URI: http://eprints.soton.ac.uk/id/eprint/462354
PURE UUID: 914ce4f3-0d95-4888-8661-b050879a1cb6
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Date deposited: 04 Jul 2022 19:06
Last modified: 04 Jul 2022 19:06
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Author:
Nahid Gamal Ibrahim El-Sharkaway
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