Buildings and combinatorial representation theory

March 26 to March 30, 2007

at the

American Institute of Mathematics, Palo Alto, California

organized by

Michael Kapovich, Arun Ram, and Monica Vazirani

This workshop, sponsored by AIM and the NSF, 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.

The workshop will differ from typical conferences in some regards. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and parallel working sessions.

The deadline to apply for support to participate in this workshop has passed.

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