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Results tagged with lie-algebras
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user 4366
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.
2
votes
How do I stop worrying about root systems and decomposition theorems (for reductive groups)?
I don't really understand what you are asking for. Root systems are geometric objects associated to finite reflection groups. Try reading Jim Humphrey's "Reflection Groups and Coxeter Groups" for a ve …
- 1,446
12
votes
Can one easily pick out a basis of a simple Lie algebra after picking a convex order?
What you are trying to do is done in complete detail in Leclerc's paper "Dual canonical bases, quantum shuffles and q-characters" (MR) based on the paper "Standard Lyndon bases of Lie algebras and en …
- 12.9k
2
votes
Accepted
character formula for demazure modules
Ryom-Hansen, Steen(DK-CPNH)
Littelmann's refined Demazure character formula revisited. (English summary)
Sém. Lothar. Combin. 49 (2002/04), Art. B49d, 10 pp.
The review:
"The author provides a pure …
- 1,472
0
votes
Killing form vs its counterpart in a given represenation
These two forms are proportional provided $\mathfrak{g}$ is simple. For the semi-simple case, you can rescale on each of the simple factors.
- 1,472
2
votes
Accepted
Realizing higher level Fock spaces
For $\mathfrak{gl}_{\infty}$ the answer is easy, you realize the Fock space as a direct limit of polynomial representations of finite $\mathfrak{gl}_n$ modules. You can read about the construction her …
- 1,472
3
votes
Does some version of U_q(gl(1|1)) have a basis like Lusztig's basis for \dot{U(sl_2)}?
Kashiwara has developed some crystal theoretic methods for the Lie superalgebra $\mathfrak{q}(n)$. However, I think you should look at Khovanov, to get an idea of what it should look like.
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