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1. Loubert, Joseph. Affine Cellularity of Finite Type KLR Algebras, and Homomorphisms Between Specht Modules for KLR Algebras in Affine Type A.

Degree: PhD, Department of Mathematics, 2015, University of Oregon

This thesis consists of two parts. In the first we prove that the Khovanov-Lauda-Rouquier algebras R_α of finite type are (graded) affine cellular in the sense of Koenig and Xi. In fact, we establish a stronger property, namely that the affine cell ideals in R_α are generated by idempotents. This in particular implies the (known) result that the global dimension of R_α is finite. In the second part we use the presentation of the Specht modules given by Kleshchev-Mathas-Ram to derive results about Specht modules. In particular, we determine all homomorphisms from an arbitrary Specht module to a fixed Specht module corresponding to any hook partition. Along the way, we give a complete description of the action of the standard KLR generators on the hook Specht module. This work generalizes a result of James. This dissertation includes previously published coauthored material. Advisors/Committee Members: Kleshchev, Alexander (advisor).

Subjects/Keywords: Affine cellularity; KLR algebras; Specht modules

…x28;18). The goal of chapter II is to establish (graded) affine cellularity in… …is amenable to checking affine cellularity. We begin in subsection 2.2 by choosing some… …AFFINE CELLULARITY OF KLR ALGEBRAS The content of this chapter has already been published as… …algebras. Our second main theorem determines Hom(S µ , S λ ) when λ is a hook. Affine… …Cellularity of KLR Algebras of Finite Types The content of chapter II has already been published as… 

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

APA (6th Edition):

Loubert, J. (2015). Affine Cellularity of Finite Type KLR Algebras, and Homomorphisms Between Specht Modules for KLR Algebras in Affine Type A. (Doctoral Dissertation). University of Oregon. Retrieved from http://hdl.handle.net/1794/19255

Chicago Manual of Style (16th Edition):

Loubert, Joseph. “Affine Cellularity of Finite Type KLR Algebras, and Homomorphisms Between Specht Modules for KLR Algebras in Affine Type A.” 2015. Doctoral Dissertation, University of Oregon. Accessed October 01, 2020. http://hdl.handle.net/1794/19255.

MLA Handbook (7th Edition):

Loubert, Joseph. “Affine Cellularity of Finite Type KLR Algebras, and Homomorphisms Between Specht Modules for KLR Algebras in Affine Type A.” 2015. Web. 01 Oct 2020.

Vancouver:

Loubert J. Affine Cellularity of Finite Type KLR Algebras, and Homomorphisms Between Specht Modules for KLR Algebras in Affine Type A. [Internet] [Doctoral dissertation]. University of Oregon; 2015. [cited 2020 Oct 01]. Available from: http://hdl.handle.net/1794/19255.

Council of Science Editors:

Loubert J. Affine Cellularity of Finite Type KLR Algebras, and Homomorphisms Between Specht Modules for KLR Algebras in Affine Type A. [Doctoral Dissertation]. University of Oregon; 2015. Available from: http://hdl.handle.net/1794/19255

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