Categorical Actions on Supercategory O
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Date
2016-11-21
Authors
Davidson, Nicholas
Journal Title
Journal ISSN
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Publisher
University of Oregon
Abstract
This dissertation uses techniques from the theory of categorical actions of Kac-Moody algebras to study the analog of the BGG category O for the queer Lie superalgebra. Chen recently reduced many questions about this category to its so-called types A, B, and C blocks. The type A blocks were completely described in joint work with Brundan in terms of the general linear Lie superalgebra. This dissertation proves that the type C blocks admit the structure of a tensor product categorification of the n-fold tensor power of the natural sp_\infty-module. Using this result, we relate the combinatorics for these blocks to Webster’s orthodox bases for the quantum group of type C_\infty, verifying the truth of a recent conjecture of Cheng-Kwon-Wang. This dissertation contains coauthored material.
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Keywords
Categorification, Kac-Moody, Representation Theory, Superalgebra, Supercategorification, Supercategory