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Results tagged with rt.representation-theory
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user 80467
Linear representations of algebras and groups, Lie theory, associative algebras, multilinear algebra.
1
vote
1
answer
221
views
Two different formulations of the Bott–Samelson resolution
There seem to be two formulations of the Bott–Samelson resolution flowing around. For concreteness, let $ G = \mathrm{GL}_{n} ( \mathbb{C} ) $ with the Borel subgroup $ B \subset G $ of upper triangul …
- 295
1
vote
0
answers
200
views
Visualizing the affine Bruhat decomposition for $\operatorname{SL}_2$
$
\newcommand\Fl{\mathcal{F}\!\ell}
\newcommand\numC{\mathbb{C}}
\newcommand\numZ{\mathbb{Z}}
\newcommand\ringO{\mathbb{O}}
\newcommand\ringK{\mathbb{K}}
\newcommand\power{\num …
- 295
0
votes
Accepted
Two different formulations of the Bott–Samelson resolution
I was being stupid. Of course, as @LSpice also remarks, the real map is
\begin{align*}
B\backslash P_{i_1} \times^B \dotsb \times^B P_{i_k}/B
& \longrightarrow
\bigl( G/B \times_{G/P_{i_1}}\dotsb \tim …
- 295