Title: qRSt: A probabilistic Robinson--Schensted correspondence for Macdonald polynomials
| Speaker: | Florian Aigner |
| Affiliation: | Université du Québec à Montréal |
| Zoom: | Contact Karen Yeats |
Abstract:
The
Robinson--Schensted
(RS)
correspondence
is
a
bijection
between
permutations
and
pairs
of
standard
Young
tableaux
which
plays
a
central
role
in
the
theory
of
Schur
polynomials.
In
this
talk,
I
will
present
a
(q,t)-dependent
probabilistic
deformation
of
Robinson--Schensted
which
is
related
to
the
Cauchy
identity
for
Macdonald
polynomials.
By
specialising
q
and
t,
one
recovers
the
row
and
column
insertion
algorithm
as
well
as
q-
and
t-deformations
of
RS;
these
have
been
introduced
in
recent
years
and
are
related
to
q-Whittaker
and
Hall-Littwood
polynomials
respectively.
I
will
also
explain
connections
to
a
(q,t)-generalization
of
the
Greene--Nijenhuis--Wilf
random
hook
walk
and
the
q-Plancherel
measure.
This
is
joint
work
with
Gabriel
Frieden.