Amadou Keita
Published 2018-12-03Version 1
The most famous simple Lie algebra is $sl_n$ (the $n \times n$ matrices with trace equals $0$). The representation theory for $sl_n$ has been one of the most important research areas for the past hundred years and within their the simple finite-dimensional modules have become very important. They are classified and Gelfand and Tsetlin actually gave an explicit construction of a basis for every simple module. We extend it by providing theorems and proofs, and construct monomial bases of the simple module.
On The Cohomology of $\mathrm{SL}_2$ with Coefficients in a Simple Module
On centers of blocks with one simple module
Laurent phenomenon and simple modules of quiver Hecke algebras
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