Branching laws for tensor modules over classical locally finite Lie algebras

  • Given an embedding of a Lie algebra g' into a Lie algebra g and an irreducible g-module M, the branching problem is to determine the structure of M as a module over g'. In this thesis, we consider the case when both g' and g are classical locally finite Lie algebras (embeddings of such Lie algebras have been described by I. Dimitrov and I. Penkov) and M is a simple tensor g-module (the class of tensor modules has been introduced and studied in a series of papers by E. Dan-Cohen, I. Penkov, V. Serganova, and K. Styrkas). The goal of the thesis is to solve the branching problem for such triples g', g, and M. Since M is in general a not completely reducible g'-module, we determine the socle filtration of M over g'. Due to the description of embeddings of classical locally finite Lie algebras given by I. Dimitrov and I. Penkov, when g' is simple our result holds for all possible embeddings of g' into g.

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Publishing Institution:IRC-Library, Information Resource Center der Jacobs University Bremen
Granting Institution:Jacobs Univ.
Author:Elitza Hristova
Referee:Ivan Penkov, Alan Huckleberry, Keivan Mallahi-Karai, Ivan Dimitrov
Advisor:Ivan Penkov
Persistent Identifier (URN):urn:nbn:de:101:1-201307119353
Document Type:PhD Thesis
Date of Successful Oral Defense:2013/02/01
Date of First Publication:2013/02/13
PhD Degree:Mathematics
School:SES School of Engineering and Science
Other Countries Involved:Canada
Library of Congress Classification:Q Science / QA Mathematics (incl. computer science) / QA150-272.5 Algebra
Call No:Thesis 2013/1

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