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Apr 26, 2020 at 6:02 comment added Monty @May I ask you one more? Is there a similar involution Weyl group action for other classical group like symplectic group?
Apr 25, 2020 at 17:41 comment added Monty Thank you very much! The reference you informed me is the very one I am searching for. There is another action like taking contragredient representation. But I am still wondering why for $GL(n)$, there is no such involution action but only permutation. Do you know some intuitive reason for why there does not Weyl group element corresponding to taking $g^{-1}$ to each components of $GL(n_i)$?
Apr 23, 2020 at 23:49 vote accept Monty
Apr 18, 2020 at 19:30 comment added LSpice This seems to answer the converse of the question.
Apr 18, 2020 at 19:05 comment added Not a grad student Thanks. There are several papers by David Goldberg with similar titles.
Apr 18, 2020 at 19:04 history edited Not a grad student CC BY-SA 4.0
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Apr 18, 2020 at 18:46 comment added Mikhail Borovoi The reference in the answer has no page 1272.
Apr 18, 2020 at 18:15 history answered Not a grad student CC BY-SA 4.0