Meng, Matthias
(2010).
Compression of Nakajima monomials in type A and C.
PhD thesis, Universität zu Köln.
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Abstract
We describe an explicit crystal morphism between Nakajima monomials and monomials which give a realization of crystal bases for nite dimensional irreducible modules over the quantized enveloping algebra for Lie algebras of type A and C. This morphism provides a connection between arbitrary Nakajima monomials and Nakashima Kashiwara tableaux. This yields a translation of Nakajima monomials to the Littelmann path model. Furthermore, as an application of our results we dene an insertion scheme for Nakajima monomials compatible to the insertion scheme for tableaux.
| Item Type: | Thesis (PhD thesis) |
| Translated title: | Title Language Komprimierung von Nakajima Monomen in Typ A und C German Compression of Nakajima monomials in type A and C English |
| Translated abstract: | Abstract Language Wir beschreiben für Lie-Algebren vom Typ A und C einen expliziten Kristallmorphismus zwischen Nakajima Monomen und Monomen, die eine Realisierung von kristallinen Basen von endlich dimensionalen irreduziblen Moduln der quantisierten universell einhüllenden Algebra bilden. Dieser Morphismus liefert eine Verbindung zwischen beliebigen Nakajima Monomen und Nakashima Kashiwara Tableaux, welche zu einer Übersetzung zwischen Nakajima Monomen und dem Wege-Modell von Littelmann führt. Außerdem denieren wir als eine Anwendung unserer Ergebnisse ein "Insertion scheme" für Nakajima Monome, das kompatibel mit dem "Insertion scheme" für Tableaux ist. German |
| Creators: | Creators Email ORCID ORCID Put Code Meng, Matthias m.meng@web.de UNSPECIFIED UNSPECIFIED |
| URN: | urn:nbn:de:hbz:38-32952 |
| Date: | 2010 |
| Language: | English |
| Faculty: | Faculty of Mathematics and Natural Sciences |
| Divisions: | Faculty of Mathematics and Natural Sciences > Department of Mathematics and Computer Science > Mathematical Institute |
| Subjects: | Mathematics |
| Date of oral exam: | 24 January 2011 |
| Referee: | Name Academic Title Littelmann, Peter Prof. Dr. |
| Refereed: | Yes |
| URI: | http://kups.ub.uni-koeln.de/id/eprint/3295 |
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