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You searched for +publisher:"University of Colorado" +contributor:("Farid Aliniaeifard"). Showing records 1 – 2 of 2 total matches.

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University of Colorado

1. Ly, Megan Danielle. Schur – Weyl Duality for Unipotent Upper Triangular Matrices.

Degree: PhD, 2018, University of Colorado

Schur – Weyl duality is a fundamental framework in combinatorial representation theory. It intimately relates the irreducible representations of a group to the irreducible representations of its centralizer algebra. We investigate the analogue of Schur – Weyl duality for the group of unipotent upper triangular matrices over a finite field. In this case, the character theory of these upper triangular matrices is "wild" or unattainable. Thus we employ a generalization, known as supercharacter theory, that creates a striking variation on the character theory of the symmetric group with combinatorics built from set partitions. In this thesis, we present a combinatorial formula for calculating a restriction and induction of supercharacters based on statistics of set partitions and seashell inspired diagrams. We use these formulas to create a graph that encodes the decomposition of a tensor space, and develop an analogue of Young tableaux, known as shell tableaux, to index paths in this graph. These paths also help determine a basis for the maps that centralize the action of the group of unipotent upper triangular matrices. We construct a part of this basis by determining copies of certain modules inside a tensor space to construct projection maps onto supermodules that act on a standard basis. Advisors/Committee Members: Nathaniel Thiem, Richard M. Green, Martin Walter, Amanda Schaeffer Fry, Farid Aliniaeifard.

Subjects/Keywords: supercharacter; schur-weyl duality; matrices; theory; combinatiorial; Mathematics; Statistical Theory

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APA (6th Edition):

Ly, M. D. (2018). Schur – Weyl Duality for Unipotent Upper Triangular Matrices. (Doctoral Dissertation). University of Colorado. Retrieved from https://scholar.colorado.edu/math_gradetds/59

Chicago Manual of Style (16th Edition):

Ly, Megan Danielle. “Schur – Weyl Duality for Unipotent Upper Triangular Matrices.” 2018. Doctoral Dissertation, University of Colorado. Accessed November 27, 2020. https://scholar.colorado.edu/math_gradetds/59.

MLA Handbook (7th Edition):

Ly, Megan Danielle. “Schur – Weyl Duality for Unipotent Upper Triangular Matrices.” 2018. Web. 27 Nov 2020.

Vancouver:

Ly MD. Schur – Weyl Duality for Unipotent Upper Triangular Matrices. [Internet] [Doctoral dissertation]. University of Colorado; 2018. [cited 2020 Nov 27]. Available from: https://scholar.colorado.edu/math_gradetds/59.

Council of Science Editors:

Ly MD. Schur – Weyl Duality for Unipotent Upper Triangular Matrices. [Doctoral Dissertation]. University of Colorado; 2018. Available from: https://scholar.colorado.edu/math_gradetds/59


University of Colorado

2. Lamar, Jonathan P. Lattices of Supercharacter Theories.

Degree: PhD, 2018, University of Colorado

The set of supercharacter theories of a finite group forms a lattice under a natural partial order. An active area of research in the study of supercharacter theories is the classification of this lattice for various families of groups. One other active area of research is the formation of Hopf structures from compatible supercharacter theories over indexed families of groups. This thesis therefore has two goals. First, we will classify the supercharacter theory lattice of the dihedral groups <i>D</i>2n in terms of their cyclic subgroups of rotations, as well as for some semidirect products of the form ℤ<sub><i>n</i></sub> ⋊ ℤ<sub><i>p</i></sub>. Second, we will construct a pair of combinatorial Hopf algebras from natural supercharacter theories on the alternating and finite special linear groups and relate them using the theory of combinatorial Hopf algebras, as developed by Aguiar, Bergeron, and Sottile in 2006. Advisors/Committee Members: Nathaniel Thiem, Farid Aliniaeifard, Richard Green, Martin Walter.

Subjects/Keywords: character theory; hopf algebras; supercharacters; semidirect product; structures; Algebra; Mathematics

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Lamar, J. P. (2018). Lattices of Supercharacter Theories. (Doctoral Dissertation). University of Colorado. Retrieved from https://scholar.colorado.edu/math_gradetds/60

Chicago Manual of Style (16th Edition):

Lamar, Jonathan P. “Lattices of Supercharacter Theories.” 2018. Doctoral Dissertation, University of Colorado. Accessed November 27, 2020. https://scholar.colorado.edu/math_gradetds/60.

MLA Handbook (7th Edition):

Lamar, Jonathan P. “Lattices of Supercharacter Theories.” 2018. Web. 27 Nov 2020.

Vancouver:

Lamar JP. Lattices of Supercharacter Theories. [Internet] [Doctoral dissertation]. University of Colorado; 2018. [cited 2020 Nov 27]. Available from: https://scholar.colorado.edu/math_gradetds/60.

Council of Science Editors:

Lamar JP. Lattices of Supercharacter Theories. [Doctoral Dissertation]. University of Colorado; 2018. Available from: https://scholar.colorado.edu/math_gradetds/60

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