New descriptions of Demazure tableaux and right keys, with applications to convexity Public Deposited
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- Last Modified
- March 21, 2019
Willis, Matthew J.
- Affiliation: College of Arts and Sciences, Department of Mathematics
- 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.
- Date of publication
- May 2012
- Resource type
- Rights statement
- In Copyright
- ... in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Mathematics.
- Proctor, Robert
- Degree granting institution
- University of North Carolina at Chapel Hill
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|New descriptions of Demazure tableaux and right keys, with applications to convexity||2019-04-10||Public||