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Christian Smith, NC State, The Algebra of “up-operators” for Young’s Lattice and Bruhat Order on S_n
September 27, 2019 | 11:45 am - 12:45 pm EDT
Let be a free associative algebra over
generated by
for
in some indexing set
and let
be a poset. For
and
we define an action of
on
(the complex vector space with basis
) in a way such that
either annihilates
or sends it to
where
covers
and we extend multiplicatively and linearly. Let
be the two-sided ideal which annihilates all elements of
. We characterize
when
is Young’s Lattice and we discuss the case when
is the Bruhat Order on
.