Title: Tokuyama's identity, Schur functions, and the six vertex model
| Speaker: | Angele Hamel |
| Affiliation: | Wilfred Laurier University |
| Room: | MC 5501 |
Abstract:
In
1988
Tokuyama
discovered
a
remarkable
identity
that
expresses
a
certain
combinatorial
sum
as
the
product
of
a
t-deformed
Vandermonde
determinant
and
Schur
symmetric
function.
His
identity
is
a
modern
twist
on
Weyl's
character
formula
—
a
well-known
classical
algebraic
identity
introduced
by
Hermann
Weyl
in
the
1920s.
The
algebraic
and
combinatorial
proofs
of
Tokuyama's
identity
involve
symmetric
functions,
tableaux,
Gelfand-Tsetlin
patterns,
and
determinants,
and
they
reveal
much
about
the
structure
of
these
objects.
In
this
talk
I
will
present
connections
to
number
theory
and
the
six
vertex
model,
along
with
some
recent
combinatorial
results
for
symplectic
characters
and
for
factorial
Schur
functions.