Counting factorization of Coxeter elements into products of reflections
Speaker: | Guillaume Chapuy |
---|---|
Affiliation: | LIAFA, France |
Room: | Mathematics and Computer Building (MC) 5158 |
Abstract:
A
classical
formula
asserts
that
the
number
of
factorizations
of
the
full
cycle
(1,2,...,n)
into
(n-1)
transpositions
is
n(n-2).
I
will
talk
about
two
generalizations
of
this
result.
The
first
one
deals
with
factorizations
of
"higher
genus",
i.e.
into
(n-1+2g)
transpositions
for
g>0.
It
is
due
to
Shapiro,
Shapiro
and
Vainshtein
in
the
context
of
Hurwitz
numbers.
The
second
one,
where
one
replaces
the
symmetric
group
Sn
by
any
finite
subgroup
of
GLn
generated
by
reflections,
and
the
long
cycle
by
a
"Coxeter
element"
is
due
to
Deligne,
and
Bessis.
I
will
then
present
our
new
result,
that
generalizes
both
results
simultaneously:
we
treat
the
case
of
"higher
genus"
factorizations
in
arbitrary
well-generated
complex
reflection
groups
(in
particular,
in
finite
Coxeter
groups).
Joint
work
with
Christian
Stump,
Hanover.