Weyl Group - Analogy With Algebraic Groups

Analogy With Algebraic Groups

Main article: q-analog See also: Field with one element

There are a number of analogous results between algebraic groups and Weyl groups – for instance, the number of elements of the symmetric group is n!, and the number of elements of the general linear group over a finite field is the q-factorial ; thus the symmetric group behaves as though it were a linear group over "the field with one element". This is formalized by the field with one element, which considers Weyl groups to be simple algebraic groups over the field with one element.

Read more about this topic:  Weyl Group

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