Buildings and combinatorial representation theory

March 26 to March 30, 2007

at the

American Institute of Mathematics, San Jose, California

organized by

Michael Kapovich, Arun Ram, and Monica Vazirani

Original Announcement

This workshop will bring together researchers representing different perspectives in combinatorial representation theory: combinatorial, metric, and algebro-geometric.

It has emerged from recent works of Littelmann-Gaussent, Kapovich-Leeb-Millson, Haines, and others, that Bruhat--Tits buildings play an essential, not yet well-understood role in combinatorial representation theory by providing a geometric realization to existing combinatorial models and linking them to the algebro-geometric tools of representation theory.

In particular the workshop goals include examining and comparing the different approaches to the saturation theorem, with an emphasis on the role of buildings, to get more precise answers (in all types) and improve the proofs, and possibly also make a sensible Horn conjecture in other types.

We further aim to understand the different combinatorial models involved (such as Knutson-Tao honeycombs, MV polytopes, Littelmann path models, canonical bases), provide a dictionary between them, and lay the groundwork to enable researchers to apply these tools toward a host of related problems.

Material from the workshop

A list of participants.

The workshop schedule.

A report on the workshop activities.

Lecture notes

Some references

Other related information

For your entertainment (or challenge).

Papers arising from the workshop:

Stability inequalities and universal Schubert calculus of rank 2
by  Arkady Berenstein and Michael Kapovich
Affine buildings for dihedral groups
by  Arkady Berenstein and Michael Kapovich