Combinatorics and complexity of Kronecker coefficients
November 3 to November 7, 2014
American Institute of Mathematics,
Palo Alto, California
and Ernesto Vallejo
This workshop will be devoted to the study of Kronecker coefficients which describe the
decomposition of tensor products of irreducible representations of a
symmetric group into irreducible representations. We concentrate on
their combinatorial interpretation, computational aspects and
applications to other fields.
The workshop will focus on:
- Finding combinatorial interpretation for the Kronecker
coefficients. In terms of complexity theory this amounts to working on
resolving whether the problem $KRON$ is in $\#P$. The aim will be to use
complexity theory to find evidence for or against that.
- Determining the complexity of deciding the problem $KP$ of
positivity of the Kronecker coefficients. Mulmuley's conjecture
states that $KP$ is in $P$. The goal will be to either prove this
conjecture or else show that, for example, $KP$ is $NP$--hard.
- Resolving combinatorial special cases. Among them are
proving the Saxl conjecture that for every large enough symmetric
group has an irreducible representation whose tensor square contains
every irreducible representation as a constituent. Other interesting
combinatorial aspects include the application of Kronecker
coefficients to solving combinatorial problems of different origins,
specifically proving unimodality results.
Material from the workshop
A list of participants.
The workshop schedule.
A report on the workshop activities.
Papers arising from the workshop: