Mixing
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Embedding of Riemannian symmetric spaces $E_I$ and $E_{IV}$ into $E_6$ Lie group
$begingroup$
In answer and comments to this mathoverflow question we have discussed possiblity of embedding Riemmanian symmetric spaces $E_I, E_{II}, E_{III},E_{IV}$ of dimension $42,40,32,26$ respectively into $E_6$ Lie group. Spaces $E_{II}$ and $E_{III}$ can be embedded as set $M={x^2=1}$ having $12$ and $16$ dimensions of eigenspaces with eigenvalue $-1$. Consider set $P={x^2 in E_{III}}$ in Lie group $E_6$. Is there chance to find $E_I$ or $E_{IV}$ in $P$ ?
The hint is $Spin_{10}$ subgroup and grassmanians which can be found in set ${x^2=-1}$ in Clifford algebra.
lie-groups symmetric-spaces
asked Jan 23 at 14:49
Marek MitrosMarek Mitros
367212
$endgroup$
add a comment |
$begingroup$
In answer and comments to this mathoverflow question we have discussed possiblity of embedding Riemmanian symmetric spaces $E_I, E_{II}, E_{III},E_{IV}$ of dimension $42,40,32,26$ respectively into $E_6$ Lie group. Spaces $E_{II}$ and $E_{III}$ can be embedded as set $M={x^2=1}$ having $12$ and $16$ dimensions of eigenspaces with eigenvalue $-1$. Consider set $P={x^2 in E_{III}}$ in Lie group $E_6$. Is there chance to find $E_I$ or $E_{IV}$ in $P$ ?
The hint is $Spin_{10}$ subgroup and grassmanians which can be found in set ${x^2=-1}$ in Clifford algebra.
lie-groups symmetric-spaces
asked Jan 23 at 14:49
Marek MitrosMarek Mitros
367212
$endgroup$
add a comment |
$begingroup$
In answer and comments to this mathoverflow question we have discussed possiblity of embedding Riemmanian symmetric spaces $E_I, E_{II}, E_{III},E_{IV}$ of dimension $42,40,32,26$ respectively into $E_6$ Lie group. Spaces $E_{II}$ and $E_{III}$ can be embedded as set $M={x^2=1}$ having $12$ and $16$ dimensions of eigenspaces with eigenvalue $-1$. Consider set $P={x^2 in E_{III}}$ in Lie group $E_6$. Is there chance to find $E_I$ or $E_{IV}$ in $P$ ?
The hint is $Spin_{10}$ subgroup and grassmanians which can be found in set ${x^2=-1}$ in Clifford algebra.
lie-groups symmetric-spaces
asked Jan 23 at 14:49
Marek MitrosMarek Mitros
367212
$endgroup$
In answer and comments to this mathoverflow question we have discussed possiblity of embedding Riemmanian symmetric spaces $E_I, E_{II}, E_{III},E_{IV}$ of dimension $42,40,32,26$ respectively into $E_6$ Lie group. Spaces $E_{II}$ and $E_{III}$ can be embedded as set $M={x^2=1}$ having $12$ and $16$ dimensions of eigenspaces with eigenvalue $-1$. Consider set $P={x^2 in E_{III}}$ in Lie group $E_6$. Is there chance to find $E_I$ or $E_{IV}$ in $P$ ?
The hint is $Spin_{10}$ subgroup and grassmanians which can be found in set ${x^2=-1}$ in Clifford algebra.
lie-groups symmetric-spaces
lie-groups symmetric-spaces
asked Jan 23 at 14:49
Marek MitrosMarek Mitros
367212
asked Jan 23 at 14:49
Marek MitrosMarek Mitros
367212
edited Jan 25 at 11:00
Marek Mitros
asked Jan 23 at 14:49
Marek MitrosMarek Mitros
367212
asked Jan 23 at 14:49
Marek MitrosMarek Mitros
367212
asked Jan 23 at 14:49
Marek MitrosMarek Mitros
367212
367212
add a comment |
add a comment |
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