Equivariant Projection Morphisms of Specht Modules
| dc.contributor.author | Mohammed, Tagreed | |
| dc.contributor.examiningcommittee | Kocay, William (Computer Scince) Krause, Guenter (Mathematics) Stokke, Anna (University of Winnipeg) | en |
| dc.contributor.supervisor | Chipalkatti, Jaydeep (Mathematics) | en |
| dc.date.accessioned | 2009-09-04T19:11:28Z | |
| dc.date.available | 2009-09-04T19:11:28Z | |
| dc.date.issued | 2009-09-04T19:11:28Z | |
| dc.degree.discipline | Mathematics | en_US |
| dc.degree.level | Master of Science (M.Sc.) | en_US |
| dc.description.abstract | This thesis is devoted to a problem in the representation theory of the symmetric group over C (the field of the complex numbers). Let d be a positive integer, and let S_d denote the symmetric group on d letters. Given a partition k of d, the Specht module V_k is a finite dimensional vector space over C which admits a natural basis indexed by all standard tableaux of shape k with entries in {1, 2, ..., d}. It affords an irreducible representation of the symmetric group S_d, and conversely every irreducible representation of S_d is isomorphic to V_k for some partition k. Given two Specht modules V_k, V_t their tensor product representation is in general reducible, and hence it splits into a direct sum of irreducibles. This raises the problem of describing the S_d equivariant projection morphisms (alternately called S_d-homomorphisms) in terms of the standard tableaux basis. In this work we give explicit formulae describing this morphism in the following cases: k=(d-1, 1), (d-2, 1,1), (2, 1,... ,1). Finally, we present a conjecture formula for the q-morphism in the case k=(d-r, 1, ..., 1). | en |
| dc.description.note | May 2009 | en |
| dc.format.extent | 379353 bytes | |
| dc.format.mimetype | application/pdf | |
| dc.identifier.uri | http://hdl.handle.net/1993/3190 | |
| dc.language.iso | eng | en_US |
| dc.rights | open access | en_US |
| dc.subject | Representations | en |
| dc.subject | characters | en |
| dc.subject | Tableaux | en |
| dc.subject | Specht-morphisms | en |
| dc.subject | Equivariant-morphisms | en |
| dc.subject | Q-forms | en |
| dc.title | Equivariant Projection Morphisms of Specht Modules | en |
| dc.type | master thesis | en_US |