Symmetric functions and infinite dimensional algebras
Baker, TH (1994) Symmetric functions and infinite dimensional algebras. PhD thesis, University of Tasmania. AbstractInfinitedimensional algebras and symmetric functions arise in many diverse areas of mathematics and physics. In this thesisseveral problems in these two areas are
studied.
We investigate the concept of replicated and qreplicated arguments in Schur and HallLittlewood symmetric functions. A description of "dual" compound symmetric functions is obtained with the help of functions of a replicated argument, while Schur and HallLittlewood functions of a qreplicated argument are both shown to be related to Macdonald's symmetric functions.
Various tensor product decompositions and winding subalgebra branching rules for the N = 1 and N = 2 superconformal algebras are examined by using the triple
and quintuple product identities and various generalizations thereof, concentrating on the particular cases when these decompositions are finite or multiplicity free.
The bosonfermion correspondence is utilized to develop an algorithm for the calculation of outer products of Schur and Qfunctions with power sum symmetric functions, and general (outer) multiplication of Sfunctions. A procedure is also developed for the evaluation of (outer) plethysms of Schur functions and power sums. A few examples are given which demonstrate the usefulness of this method for calculating plethysms between Schur functions. By examining the vertex operator realization of HallLittlewood functions we are also able to generate an algorithm for expressing HallLittlewood functions in terms of Schur functions. The operation of outer
plethysm is defined for HallLittlewood functions and the algorithm developed for Sfunctions is extended to this case as well.
Item Type:  Thesis (PhD) 

Additional Information:  Copyright the Author 

Keywords:  symmetric functions, infinite
dimensional algebras 

ID Code:  8557 

Deposited By:  Mrs TM Riley 

Deposited On:  06 Apr 2009 12:17 

Last Modified:  20 Oct 2012 15:13 

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