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2
votes
1answer
98 views

When does an irreducible G-module admit an invariant quadratic form of signature (n,n+1)

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 ...
4
votes
2answers
419 views

Malcev Lie algebra and associated graded Lie algebra

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 \...
3
votes
3answers
495 views

About $G$-modules versus $Lie(G)$-modules for algebraic groups

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'...
7
votes
2answers
706 views

Does there exist a complex Lie group G such that …

... every Riemann surface of genus $1$ appears as a complex one-parameter subgroup of $G$?