Motivating a q-Version of the Embedding Between the Categories Heis and Par(t)

Undergraduate Honors Thesis

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Citeable URL: https://scholar.colorado.edu/concern/undergraduate_honors_theses/w37637955

Abstract

Within this work, assuming an undergraduate background, we will introduce the material necessary to understand five categories and their relationships. These include the Heisenberg category Heis, the partition category Par(t), the category of kSn-modules Sn-mod, the q-deformed Heisenberg category Heis(q), and GLn(Fq)-mod. The main aim of the work done in this paper is to motivate a generalization of a particular isomorphism of functors constructed by Likeng and Savage between the non-q-deformed categories Par(n), Heis↑↓(n), and Sn-mod to a similar isomorphism between functors on their q- deformed counterparts. We offer a conjectured embedding into Heis↑↓(q) and demonstrate which relations of the partition category are respected by the embedding.

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