Using Gram matrices and residues to generate symmetric functions Public Deposited

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Last Modified
  • March 20, 2019
Creator
  • Behrend, Samuel
    • Affiliation: College of Arts and Sciences, Department of Mathematics
Abstract
  • In this paper we argue for the use of a symmetric bilinear map S on Qn+1 as a means of producing and manipulating symmetric functions; using certain vectors of rational functions we can produce Schur functions. We define S as the determinant of a specific Gram matrix, whose elements are the result of an antisymmetric bilinear map on Q as well as a reversion map R on the same space. Ultimately, S allows us to derive an alternative construction of the Jacobi-Trudi identity (extending the identity to Schur functions) as well as a variant of the Cauchy identities.
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  • In Copyright
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  • ... in partial fulfillment of the requirements for the degree of Master of Science in the Department of Mathematics.
Advisor
  • Rimanyi, Richard
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