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How to find all reduced expression of the longest element in a Weyl group?

asked 2021-11-08 17:35:19 +0100

lijr07 gravatar image

Let $W$ be a Weyl group. How to find reduced expression of the longest element $w_0 \in W$ in SageMath?

I can define

W = WeylGroup(["E", 6])
w0=W.long_element().reduced_word()

Then I got one reduced expression of $w_0$. But how to obtain all reduced expression of $w_0$? Thank you very much.

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answered 2021-11-08 19:49:38 +0100

FrédéricC gravatar image

Nihao.

Like that

sage: W = WeylGroup(["A", 4])
sage: w0 = W.long_element()
sage: w0.reduced_words()

Tab-completion is your friend : w0.red<TAB>

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@FrédéricC, thank you very much!

lijr07 gravatar imagelijr07 ( 2021-11-08 20:14:57 +0100 )edit

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Asked: 2021-11-08 17:35:19 +0100

Seen: 23 times

Last updated: Nov 08 '21