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Results tagged with lie-groups
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user 1528
Lie Groups are Groups that are additionally smooth manifolds such that the multiplication and the inverse maps are smooth.
1
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11
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What would you want on a Lie theory cheat poster?
Handy identities for rings associated to Lie groups and algebraic groups, such as the enveloping algebra, hyperalgebra, or quantum groups of various kinds. For example, I often find myself needing to …
3
votes
1
answer
557
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Springer isomorphisms and parabolics
Let $G$ be a semisimple, simply-connected algebraic group over an algebraically closed field $k$ of positive characteristic. Fix a Borel subgroup $B \subseteq G$ with unipotent radical $U$. Also let $ …
- 3,637
2
votes
Stratifications and Cohomology Computations
I don't know if this is the direction you're interested in, but the book "An Introduction to Intersection Homology Theory" by Kirwan and Woolf is a nice readable book that has a lot about stratificati …
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4
votes
subgroups with the same number of roots that the group.
A good modern introduction to the subject is given in Martin Liebeck's survey article "Introduction to the subgroup structure of algebraic groups." It's a chapter in the book "Representations of Reduc …
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3
votes
1
answer
121
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Lower bound on the degree of a product of elements in a hyperalgebra/enveloping algebra
Background:
Fix a linear algebraic group $G$ over an algebraically closed field $k$ of arbitrary characteristic and let $B \subseteq G$ be a Borel subgroup with unipotent radical $N$. Let $\Delta^+$ d …
- 3,637
6
votes
Rep Theory Consequences of Bott--Weil--Borel
Check out the book Frobenius Splitting Methods in Representation Theory by Brion and Kumar. There are lots of representation-theoretic results in positive characteristic in that book that rely crucial …
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