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Person# Mikaël Cavallin

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Composition series

In abstract algebra, a composition series provides a way to break up an algebraic structure, such as a group or a module, into simple pieces. The need for considering composition series in the contex

Algebraic group

In mathematics, an algebraic group is an algebraic variety endowed with a group structure that is compatible with its structure as an algebraic variety. Thus the study of algebraic groups belongs bot

Module (mathematics)

In mathematics, a module is a generalization of the notion of vector space in which the field of scalars is replaced by a ring. The concept of module generalizes also the notion of abelian group, sin

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Mikaël Cavallin, Donna Testerman

Let K be an algebraically closed field of characteristic and let W be a finite-dimensional K-vector space of dimension greater than or equal to 5. In this paper, we give the structure of certain Weyl modules for in the case where , as well as the dimension of the corresponding irreducible, finite-dimensional, rational KG-modules. In addition, we determine the composition factors of the restriction of certain irreducible, finite-dimensional, rational -modules to .

2018Let be a finite-dimensional semisimple Lie algebra over having rank l and let V be an irreducible finite-dimensional -module having highest weight λ. Computations of weight multiplicities in V, usually based on Freudenthal's formula, are in general difficult to carry out in large ranks or for λ with large coefficients (in terms of the fundamental weights). In this paper, we first show that in some situations, these coefficients can be “lowered” in order to simplify the calculations. We then investigate how this can be used to improve the aforementioned formula of Freudenthal, leading to a more efficient version of the latter in terms of complexity as well as to a way of dealing with certain computations in unbounded ranks. We conclude by illustrating the last assertion with a concrete example.

2017