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2 votes
1 answer
268 views

Stabilizer of a Levi subgroup in the Weyl group and its quotient

(I appologize in advance if this question is too naive for experts, since I know very little about the geometry/combinatorics of Weyl/Coxeter groups.) For simplicity, let $G$ be a connected reductive ...
8 votes
0 answers
267 views

A Lie-theoretic question regarding $B\ltimes \mathfrak{g}/\mathfrak{b}$

I am stuck on a seeming elementary Lie-theoretic question arising from a study of components of affine Springer fibers. Will be very grateful if somebody would like to share some insight, or ...
5 votes
1 answer
505 views

How to determine a highest weight corresponding to a parabolic subgroup?

Let $G$ be a simply connected, semisimple algebraic group over $\mathbb C$ with maximal torus $T$ and Borel subgroup $B$ containing $T$. If $(V,\pi)$ is an irreducible representation of $G$, then $(V,...
2 votes
2 answers
839 views

Possible Borel subgroups of GL_n?

I am trying to understand the interaction between Borel subgroups of $GL_n$ and its roots. Is it correct to say that for any choice of roots among each pair of reciprocal roots there is a Borel ...