Schubert calculus, adjoint representation and moment polytopes
| buir.advisor | Klyachko, Alexander | |
| dc.contributor.author | Sakar, Serkan | |
| dc.date.accessioned | 2016-01-08T18:20:25Z | |
| dc.date.available | 2016-01-08T18:20:25Z | |
| dc.date.issued | 2012 | |
| dc.description | Ankara : The Department of Mathematics and the Graduate School of Engineering and Science of Bilkent University, 2012. | en_US |
| dc.description | Thesis (Master's) -- Bilkent University, 2012. | en_US |
| dc.description | Includes bibliographical references. | en_US |
| dc.description.abstract | Let Hν denote the irreducible representation of the special unitary group SU(n) corresponding to Young diagram ν and let g = su(n) denote the Lie algebra of SU(n). One can show that Hν appears in the symmetric algebra S∗ g if and only if n divides the size of the Young diagram ν. Kostant’s problem asks what is the least number N such that Hν appear in SN g. The moment polytope of the adjoint representation is the polytope generated by the normalized weights ν˜ such that Hν appears in S∗ g and it helps to put lower bounds on number N in the Kostant’s problem. In this thesis, we compute the moment polytope of the adjoint representation of SU(n) for n ≤ 9 using the solutions of the classical spectral problem and so-called ν-representability problem. | en_US |
| dc.description.provenance | Made available in DSpace on 2016-01-08T18:20:25Z (GMT). No. of bitstreams: 1 0006277.pdf: 496346 bytes, checksum: 69bef03ce2474d1996ca4c0dc19deb30 (MD5) | en |
| dc.description.statementofresponsibility | Sakar, Serkan | en_US |
| dc.format.extent | viii, 56 leaves | en_US |
| dc.identifier.uri | http://hdl.handle.net/11693/15547 | |
| dc.language.iso | English | en_US |
| dc.rights | info:eu-repo/semantics/openAccess | en_US |
| dc.subject | Kostant’s problem | en_US |
| dc.subject | level of a representation | en_US |
| dc.subject | moment polytope | en_US |
| dc.subject.lcc | QA691 .S35 2012 | en_US |
| dc.subject.lcsh | Polytopes. | en_US |
| dc.subject.lcsh | Spectral theory (Mathematics) | en_US |
| dc.title | Schubert calculus, adjoint representation and moment polytopes | en_US |
| dc.type | Thesis | en_US |
| thesis.degree.discipline | Mathematics | |
| thesis.degree.grantor | Bilkent University | |
| thesis.degree.level | Master's | |
| thesis.degree.name | MS (Master of Science) |
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