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Skip to Search Results- 4Yangians
- 2Quantum loop algebra
- 1Degenerate form
- 1Irreducible representation
- 1Lie algebras
- 1Lie superalgebras
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Fall 2023
This dissertation establishes various structural and representation theoretic results in super Yangian theory. In its first part, this dissertation details the algebraic structure and representation theory for the Yangians of orthosymplectic Lie superalgebras. Addressing these Yangians via the...
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Fall 2014
Among representation theorists, it is well known that Yangians can be realized as some type of degenerate form of quantum loop algebras. What is not well known is precisely how this degeneration takes place. In the first part of this thesis, we will demonstrate explicitly the process by which...
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Fall 2019
In the first part of this dissertation, we prove a generalization of a theorem of Drinfeld’s which allows one to rebuild the Yangian of an arbitrary simple Lie algebra starting from any of its finite-dimensional modules satisfying a non-triviality condition. This is achieved using the so-called...
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Fall 2016
The two families of quantum groups of Yangians and quantum loop algebras have a library of similar results on their structures and representation theories. Not until Gautam and Toledano-Laredo’s works in the past decade has there been an explanation for these correspondences. We present a...