Whittaker Functions, Crystal Bases, and Quantum Groups (10w5096)

Arriving in Banff, Alberta Sunday, June 6 and departing Friday June 11, 2010

Organizers

Ben Brubaker (University of Minnesota)

(Stanford University)

(City University of New York)

(University of Massachusetts Amherst)

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.