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7 votes
1 answer
280 views

Non-homogeneous line bundles over a homogeneous space

Let $G$ be a compact Lie group and $G/K$ a connected homogeneous space. A homogeneous vector bundle over $G/K$ is a vector bundle is one that is isomorphic to a vector bundle of the form $$ G \times_{\...
László Szabados's user avatar
8 votes
0 answers
228 views

What can we say about the homogeneous spaces $E_8/E_7$ and $E_7/E_6$?

For the three exceptional compact Lie groups $E_8, E_7, E_6$ we have the inclusions $$ E_6 \subseteq E_7 \subseteq E_8. $$ What can we say about the the homogeneous spaces $$ E_8/E_7, ~~~~ E_7/E_6? $$ ...
Alain Rochefort's user avatar
2 votes
1 answer
148 views

Coinvariant representative of homogeneous space cohomology

Given a compact homogeneous space $M = K/L$, consider its de Rham complex $(\Omega^*,d)$. Will every cohomology class $[\omega] \in ker(d)/im(d)$ contain a representative $\nu$ which is invariant with ...
Fofi Konstantopoulou's user avatar
3 votes
1 answer
181 views

Automorphisms of homogeneous space $F_4/P_{\{\beta_2\}}$ over the exceptional group $F_4$

Let $F_4$ be the connected, simply connected, simple, complex, linear algebraic group of type $\mathsf{F}_4$, with Dynkin diagram $$ \beta_1-\beta_2\Rightarrow\beta_3-\beta_4\,. $$ Let $P_{\{\beta_2\}}...
Christoph Mark's user avatar
1 vote
1 answer
235 views

Torus actions on $Sp(n)$-spheres

In this old question of mine https://math.stackexchange.com/questions/1651906/spheres-as-symplectic-homogeneous-spaces the presentation of spheres as symplectic group homogeneous spaces was ...
Tomasz Köner's user avatar
1 vote
1 answer
930 views

Canonical class of partial flag variety

Let $F(d_1,d_2,\ldots,d_k;n )$ be the variety of all flags $\mathbb A^{d_1} \subset\mathbb A^{d_2}\subset\ldots\subset \mathbb A^{d_k}\subset \mathbb A^{n}$. This variety has the natural maps to ...
IBazhov's user avatar
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