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Results tagged with lie-algebras
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user 22846
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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Springer Isomorphisms for Adjoint Simple Exceptional Groups
I'm trying to understand explicitly a construction of Springer isomorphisms for adjoint exceptional groups given by Bardsley and Richardson. Their construction is as follows. Let $G$ be an adjoint sim …
- 2,902
5
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Reg the motivation behind Lusztig-Vogan bijection
This isn't even vaguely an answer to your question but is more of a clarifying remark concerning the canonical quotient. Throughout I will write [Lus84] for Lusztig's orange book "Characters of reduct …
- 2,902
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Accepted
For a Weyl group, what is the connection between its exponents and lengths of its elements?
I would leave this as a comment but I don't appear to have enough reputation points for that. Just to add to Philippe's answer that you will also find this as Theorem 10.2.3 in Carter's "Simple Groups …
- 2,902
1
vote
Accepted
Degenerate representation
Suppose $V = \mathbb{R}^n$ has a basis $(e_1,\dots,e_n)$. Your assumption is that you have a family of linear maps $\lambda_1,\dots,\lambda_m \in V^*$ which are defined such that $\lambda_r(e_i) = \la …
- 2,902