Browsing Theses by Subject "representation theory"
Now showing items 1-6 of 6
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Character Polynomials and Lagrange Inversion
(University of Waterloo, 2005)In this thesis, we investigate two expressions for symmetric group characters: Kerov?s universal character polynomials and Stanley?s character polynomials. We give a new explicit form for Kerov?s polynomials, which ... -
An estimation theoretic approach to quantum realizability problems
(University of Waterloo, 2023-09-27)This thesis seeks to develop a general method for solving so-called quantum realizability problems, which are questions of the following form: under which conditions does there exist a quantum state exhibiting a given ... -
Finitary approximations of free probability, involving combinatorial representation theory
(University of Waterloo, 2023-05-18)This thesis contributes to two theories which approximate free probability by finitary combinatorial structures. The first is finite free probability, which is concerned with expected characteristic polynomials of various ... -
On the Representation Theory of Semisimple Lie Groups
(University of Waterloo, 2010-08-30)This thesis is an expository account of three central theorems in the representation theory of semisimple Lie groups, namely the theorems of Borel-Weil-Bott, Casselman-Osborne and Kostant. The first of these realizes all ... -
Partition Algebras and Kronecker Coefficients
(University of Waterloo, 2015-08-28)Classical Schur-Weyl duality relates the representation theory of the general linear group to the representation theory of the symmetric group via their commuting actions on tensor space. With the goal of studying Kronecker ... -
Symmetry, Asymmetry and Quantum Information
(University of Waterloo, 2012-09-28)It is impossible to overstate the importance of symmetry in physics and mathematics. Symmetry arguments play a central role in a broad range of problems from simplifying a system of linear equations to a deep role in ...