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14 questions
Newest Active Bountied Unanswered
3 votes
0 answers
253 views

Let $G=GL_n$, $B$ the upper triangular matrices and $T\subset G$ the diagonal matrices. $T$ acts on $G/B$ with the natural action. I have seen it stated in the literature that all $T$-invariant curves ...
cacha's user avatar
  • 861
7 votes
1 answer
358 views

Background: The first examples one sees of reductive groups over a field $k$ are $\text{GL}_n$, $\text{SL}_n$, and $\text{PGL}_n$. We all know the definitions of $\text{GL}_n$ and $\text{SL}_n$, and ...
David Schwein's user avatar
  • 1,289
0 votes
0 answers
114 views

Let $G$ be a connected simple complex Lie group and $\mathfrak{g}$ be its Lie algebra. Let us fix a root decomposition, let $\mathfrak{b}_\pm$, $\mathfrak{n}_+$ and $\mathfrak{h}$ be the corresponding ...
Grabovsky's user avatar
  • 1
4 votes
0 answers
194 views

I was wondering if $G$ is a semisimple complex algebraic group, then is the homogeneous coordinate ring of a flag variety a UFD or not?
F.H.A's user avatar
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2 votes
1 answer
164 views

I asked a similar question on math.stackexchange but did not get any responses, so I thought I'd kick it up to mathoverflow. In Crainic and Fernandes's "Integrability of Lie Brackets" (and ...
Ben MacAdam's user avatar
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3 votes
1 answer
612 views

Let $G$ be an connected reductive algebraic group over $k=\bar{\mathbb{F}_p}$. Suppose $G$ is defined over $\mathbb{F}_q$. Let $G^{F}$ be the corresponding finite group associated to $G$. Suppose $s\...
Riju's user avatar
  • 428
0 votes
0 answers
100 views

I want to know that the present results about classifications of generalized indefinite Cartan matrices. I only have known that the classifications of hyperbolic matrces.
double-function's user avatar
  • 59
8 votes
1 answer
522 views

Let $R$ be a simply-laced root system in a Euclidean vector space $E$, with inner product normalized so that every root has length $\sqrt{2}$. Let $L \subseteq E$ be the lattice spanned by $R$. Is ...
Ravi Jagadeesan's user avatar
  • 263
2 votes
1 answer
215 views

Let L1 and L2 be two Lie algebras.If U（L1）is isomorphic to U（L2）as associative algebra，then L1 is isomorphic to L2 ？
double-function's user avatar
  • 59
8 votes
0 answers
228 views

Let $\mathfrak{g}$ be a simple complex Lie algebra and let $\Delta$ be a system of positive roots relative a choice of Cartan subalgebra and $\mathfrak{b}$ the corresponding Borel subalgebra. Let $B&...
Andy Sanders's user avatar
  • 3,090
2 votes
1 answer
188 views

Let $G$ be a connected real reductive Lie group and $V$ be a finite dimensional real irreducible $G$-module. When does $V$ admit an invariant non-degenerate quadratic form of signature $(n,n+1)$? I ...
B. Collier's user avatar
  • 21
7 votes
2 answers
1k views

Suppose $L$ is a nilpotent finite-dimensional Lie algebra over $\mathbb{Q}$ of class $c$. We can define an associated graded Lie algebra to $L$ that, as a vector space, is: $$\bigoplus_{i=1}^c \...
Vipul Naik's user avatar
  • 7,500
5 votes
3 answers
825 views

Hello, I would like to know clear references about the following facts: Let $G$ be a connected algebraic group (over alg. closed field in char. 0), $Lie(G)$ its Lie algebra, $M$ a $G$-module. I don'...
Sasha's user avatar
  • 5,682
8 votes
2 answers
2k views

... every Riemann surface of genus $1$ appears as a complex one-parameter subgroup of $G$?
Alexander Moll's user avatar
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