In this thesis,we study infinite dimensional representations of the special linear Lie algebras [special characters omitted](n). These representations arise naturally from the Weyl construction eij [special characters omitted] xi[special characters omitted], where eij are the elementary matrices. (This definition of elementary matrix differs from the one in linear algebra.) Our main results provide explicit decomposition of indecomposable representations related to the Laurent polynomials [special characters omitted]. In particular, we verify that the space of degree zero of homogeneous polynomials of three variables (resp. two variables) has length 7 (resp. 3) as an [special characters omitted](3)-representation (resp. [special characters omitted](2)-representation).
|School:||San Jose State University|
|School Location:||United States -- California|
|Source:||MAI 47/05M, Masters Abstracts International|
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