All Questions
3
questions
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255
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If $G$ is an algebraic group of adjoint type, is $\alpha_s^\vee(-1)=1$?
Suppose $G$ is a semisimple algebraic group of adjoint type. If $(W,S)$ is the Coxeter system and $s\in S$, and $\alpha_s$ is a simple root with corresponding coroot $\alpha_s^\vee$, is it true that $\...
- 660
0
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1
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Why does $P_JnP_K\cap N=N_JnN_K$ in a group with split $BN$-pair?
Suppose $G$ is a group with a split $BN$-pair, and if $N_J$ is the subgroup of $N$ such that $N_J/(B\cap N)=W_J$ (the parabolic subgroup in the Weyl group $W=N/(B\cap N)$). Let $P_I$ denote a standard ...
- 571
1
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0
answers
259
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If $P_I$ is a parabolic subgroup in $GL_n(k)$, is $P_I$ conjugate to ${P_I}^-$ under some element of $W$?
Suppose $P_I$ is a standard parabolic subgroup of $GL_n(k)$ (we can assume $k$ is finite, but I doubt it matters). Is $P_I$ conjugate to the opposite parabolic ${P_I}^-$ under some element of the Weyl ...
- 1,950