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Results tagged with lie-algebras
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user 26208
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
Examples of Richardson orbit closures not having a symplectic resolution?
Just adding a reference to the literature where this question seems to have cropped up :
"Calculating canonical distinguished involutions in the affine Weyl groups" - Chmutova, Ostrik (pdf)
They ph …
- 1,073
1
vote
Truncated induction for exceptional cases
Somewhat late, but let me answer my own question here by saying that using packages like CHEVIE (built for GAP) has been the most reliable way for me to compute j-induction. I'll leave Jim's answer as …
- 1,073
2
votes
2
answers
534
views
Truncated induction for exceptional cases
In Carter's book (Finite groups of Lie type), he reviews the truncated induction procedure (called j-operation in the text) of Macdonald-Lusztig-Spaltenstein in great detail for the classical Weyl gro …
- 1,073
5
votes
3
answers
1k
views
Reg the motivation behind Lusztig-Vogan bijection
Let $G$ be an algebraic group. Choose a Borel subgroup $B$ and
a maximal Torus $T \subset B$. Let $\Lambda$ be the set of weights wrt $T$ and let $\mathfrak{g}$ be the lie algebra of $G$.
Now, conside …
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7
votes
1
answer
590
views
Motivating the existence of Canonical Bases for Representations
In Representation Theory, the theme of the existence of a canonical basis has been explored quite a lot. I will limit myself in this question to the kind of canonical bases that arise from the Geometr …
- 1,073
2
votes
0
answers
357
views
Differential of the adjoint quotient map
My question is regarding a paper by R.W Richardson titled "Derivatives of invariant polynomials on a semisimple Lie Algebra" ** . In this paper, he reports on computations of the rank of the different …
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3
votes
Kazhdan Lusztig map and Richardson orbits
This is a very nice line of thinking! But I think the question, as stated, is imprecise.
As is correctly pointed out in the question, the KL map takes you from nilpotent orbits in $\mathfrak{g}$ to …
- 1,073
4
votes
1
answer
355
views
Affine analog of the theory of sheets
In the study of adjoint orbits in a complex semi-simple lie algebra, there is a well known object known as a "sheet". These are the irreducible components of the union of orbits of the same dimension. …
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