Braid groups and symmetric groups
Bigelow, Stephen
(
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Representations of the symmetric group
are not well understood when the field
has non-zero characteristic. They are
closely related to representations of
the Hecke algebra when the parameter q
is a root of unity. Lawrence has shown
how these representations can be
defined topologically, as an action of
the braid group on the homology of
certain configuration spaces. I will
use some examples to illustrate how
this enables one to ``see'' why
representations become reducible at
some roots of unity.
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