Jenna Rajchgot, McMaster University
"Symmetric quivers and symmetric varieties"
Since
the
1980s,
mathematicians
have
found
connections
between
orbit
closures
in
type
A
quiver
representation
varieties
and
Schubert
varieties
in
type
A
flag
varieties.
For
example,
singularity
types
appearing
in
type
A
quiver
orbit
closures
coincide
with
those
appearing
in
Schubert
varieties
in
type
A
flag
varieties;
combinatorics
of
type
A
quiver
orbit
closure
containment
is
governed
by
Bruhat
order
on
the
symmetric
group;
and
formulas
for
classes
of
type
A
quiver
orbit
closures
in
torus
equivariant
cohomology
and
K-theory
can
be
expressed
in
terms
of
Schubert
polynomials,
Grothendieck
polynomials,
and
other
objects
from
Schubert
calculus.
In
this
talk,
I
will
motivate
and
recall
some
of
this
story.
I
will
then
discuss
the
related
setting
of
H.
Derksen
and
J.
Weyman's
symmetric
quivers
and
their
representation
varieties.
I
will
show
how
one
can
adapt
results
from
the
ordinary
type
A
quiver
setting
to
unify
aspects
of
the
equivariant
geometry
of
type
A
symmetric
quiver
representation
varieties
with
Borel
orbit
closures
in
corresponding
symmetric
varieties
G/K
(G
=
general
linear
group,
K
=
orthogonal
or
symplectic
group).
This
is
joint
work
with
Ryan
Kinser
and
Martina
Lanini.
MC 5501