New descriptions of Demazure tableaux and right keys, with applications to convexity

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Last Modified
  • March 21, 2019
Creator
  • Willis, Matthew J.
    • Affiliation: College of Arts and Sciences, Department of Mathematics
Abstract
  • The right key of a semistandard Young tableau is a tool used to find Demazure characters for sl subscript n(C). This thesis gives methods to obtain the right and left keys by inspection of the semistandard Young tableau. Given a partition lambda and a Weyl group element w, there is a semistandard Young tableau Y subscript lambda(w) of shape lambda that corresponds to w. The Demazure character for lambda and w is known to be the sum of the weights of all tableaux whose right key is dominated by Y subscript lambda (w). The set of all such tableaux is denoted D subscript lambda(w). Exploiting the method mentioned above for obtaining right keys, this thesis describes the entry at each location in any T in D subscript lambda(w). Lastly, we will consider D subscript lambda(w) as an integral subset of Euclidean space. The final results present a condition that is both necessary and sufficient for this subset to be convex.
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  • In Copyright
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  • ... in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Mathematics.
Advisor
  • Proctor, Robert
Degree granting institution
  • University of North Carolina at Chapel Hill
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