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On the representation theory of the alternating groups
Published 2013-03-01“…We present the basic results on the representation theory of the alternating groups. Our approach is based on Clifford theory.…”
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The representation theory of seam algebras
Published 2020-02-01“…The boundary seam algebras $\mathsf{b}_{n,k}(\beta=q+q^{-1})$ were introduced by Morin-Duchesne, Ridout and Rasmussen to formulate algebraically a large class of boundary conditions for two-dimensional statistical loop models. The representation theory of these algebras $\mathsf{b}_{n,k}(\beta=q+q^{-1})$ is given: their irreducible, standard (cellular) and principal modules are constructed and their structure explicited in terms of their composition factors and of non-split short exact sequences. …”
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The Representation Theory of Neural Networks
Published 2021-12-01“…Overall, representing neural networks through the quiver representation theory leads to 9 consequences and 4 inquiries for future research that we believe are of great interest to better understand what neural networks are and how they work.…”
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Additive higher representation theory
Published 2014“…We contribute towards this undertaking in the case of additive higher representation theory. Inspiration is drawn from Soergel bimodules which categorify the Hecke algebra.…”
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