Weight Stretching in Moduli of Parabolic Bundles and Quiver Representations Public Deposited

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Last Modified
  • March 19, 2019
Creator
  • Sherman, Cass
    • Affiliation: College of Arts and Sciences, Department of Mathematics
Abstract
  • In their 2004 paper, King, Tollu, and Toumazet consider the effects of stretching a Littlewood-Richardson coefficient by a positive integer N. When the L-R coefficient corresponding to N=1 is small (0,1,2, or 3), they conjecture simple polynomial formulas determining the L-R coefficient for all positive integers N. In this thesis, we consider generalizations of their conjecture to parabolic vector bundles and representations of quivers. In each instance, there is a polarized moduli space (M,L) with the property that the dimension of the global sections of the Nth tensor power of L scales in the same way as the corresponding generalized L-R coefficient. The "simple polynomial formulas" then translate to simple geometric descriptions of (M,L). We prove that these descriptions hold in many cases.
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Rights statement
  • In Copyright
Advisor
  • Wahl, Jonathan
  • Cherednik, Ivan
  • Rimanyi, Richard
  • Belkale, Prakash
  • Sawon, Justin
Degree
  • Doctor of Philosophy
Degree granting institution
  • University of North Carolina at Chapel Hill Graduate School
Graduation year
  • 2016
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