10w5096 Whittaker Functions, Crystal Bases, and Quantum Groups

Arriving Sunday, June 6 and departing Friday, June 11, 2010

Organizers: Ben Brubaker (Massachusetts Institute of Technology), Dan Bump (Stanford University), Gautam Chinta (City College of New York), Paul Gunnells (University of Massachusetts Amherst).

Confirmed Participants

Press Release: Whittaker Functions, Crystal Bases, and Quantum Groups

Information for Participants

Objectives

The goal of this interdisciplinary workshop is to bring together a group of researchers in number theory, combinatorial representation theory, special functions, and mathematical physics whose work shares the common theme of Whittaker functions, who are active in these areas or have professed interest in them, and who have not had a chance to come together at a single conference devoted to their study. We expect that some talks at the conference will be expository, to present overviews of the various areas to the different researchers, while other talks will present current research results. This way conference participants will quickly find common points of investigation, which could include the following natural questions:

--- What are the statistics required from crystal graphs to extend $p$-adic Whittaker descriptions to more general context (Chevalley groups, Kac-Moody groups)? What do the new identities resulting from the non-metaplectic description tell us about the underlying representation theory?

--- Can all of the deformations described above be understood in terms of various central extensions of the underlying algebraic group? Does this provide a unifying framework for understanding the above examples? --- Can we treat local fields uniformly? Is there a way of understanding similarities between archimedean and non-archimedean calculations?

--- ``Classical limit'' calculations of these deformations arise even for double cover calculations of $mathrm{SO}(2r+1)$. Is there physical meaning to these deformations? Do such deformations exist for other higher degree arithmetic covers? Why do the formulas require the quantized universal enveloping algebra and what is essentially quantum about the metaplectic group?

As recent papers and preprints indicate, the researchers active in these areas are aware of connections between their work to other fields. The time is ripe to provide an opportunity for members of these diverse fields to meet, to share ideas, and to further pursue these new developments. A workshop devoted to these topics that brings together researchers from different fields will encourage new interactions and should lead to unusual collaborations. The intimate setting of BIRS is ideal for fostering this kind of interaction, since it offers ample opportunity for discussion outside the hours of the formal program activities.