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Lie algebras are algebraic structures which were introduced to study the concept of infinitesimal transformations. The term "Lie algebra" (after Sophus Lie) was introduced by Hermann Weyl in the 1930s. In older texts, the name "infinitesimal group" is used. Related mathematical concepts include Lie groups and differentiable manifolds.
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Dominant weights appear in Discrete Series
for the split form of G_2, consider the system of positive roots so that the short root is compact and the long root is non compact, call it b, then for large n, $\lambda + \rho_n -\rho_c +nb $ is no …