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Daily Overview |
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CA1: Computer Algebra Location: D406 Session Chair: Anne Frühbis-Krüger Session Chair: Alheydis Geiger | |
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Computing Monomial Bases of Highest-Weight and Demazure Modules RWTH Aachen University, Germany For a finite-dimensional simple complex Lie algebra $\mathfrak{g}$ and its finite-dimensional irreducible representation $V(\lambda)$, finding an explicit vector space basis of $V(\lambda)$ is one of the most important questions in representation theory. In the literature, there have been many proposals, some of which are restricted to certain types or other properties. Fang-Fourier-Littelmann generalized some of these geometrically inspired approaches to essential bases, a family of monomial bases with particular convenience. We present a divide-and-conquer approach to compute such essential bases by solving the problem for smaller weights $\lambda$ and gluing the results together. In cases where this does not suffice, additional, more expensive measures have to be taken. This algorithm heavily relies on machinery from both polyhedral geometry and algebraic Lie theory, and is therefore a perfect candidate to be implemented in OSCAR. We will give some insights into the implementation and describe how we adapted it to also solve the basis finding problem for Demazure modules. | |
