Timeline for Is there a Morse theory proof of the Bruhat decomposition?
Current License: CC BY-SA 3.0
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| Feb 11, 2023 at 0:35 | comment | added | Richard Montgomery | beautifully simple! | |
| Jun 25, 2013 at 20:31 | history | edited | Liviu Nicolaescu | CC BY-SA 3.0 |
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| Apr 18, 2012 at 4:57 | history | edited | Liviu Nicolaescu | CC BY-SA 3.0 |
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| Apr 15, 2012 at 23:27 | comment | added | Liviu Nicolaescu | I actually discuss this in my book on Morse theory. | |
| Apr 15, 2012 at 13:57 | comment | added | David E Speyer | And a similar trick works for the full flag manifold. Fix $\lambda_1 > \lambda_2 > \cdots > \lambda_n$ and identify $Fl_n$ with those Hermitian matrices whose eigenvalues are $\lambda_i$. Then $H \mapsto tr(A H)$ is again the desired Morse function. (The identification between Hermitian matrices and flags is as follows: Starting with a flag $F_1 \subset F_2 \subset \cdots$, let $v_i$ be an element of $F_i$ which is orthogonal to $F_{i-1}$, this is unique up to scalar. Let $H(F_\bullet})$ have eigenvector $v_i$ with eigenvalue $\lambda_i$.) | |
| Apr 15, 2012 at 13:26 | history | answered | Liviu Nicolaescu | CC BY-SA 3.0 |