NEXT MEETING:
Friday May 10th, 35 p.m., Room 1142 (note room change!)
Ivan Cherednik (UNC Chapel Hill)
Nonsymmetric Whittaker function and
its surprising link to the PBW filtration
The symmetric qWhittaker function attracts a lot
of attention now. Its nonsymmetric generalization
and the related theory of qTodaDunkl operators
was an unexpected development, quite involved
even for A1. I will discuss our last paper with Dan
Orr devoted to this theory for arbitrary reduced root
systems (the twisted setting). Geometrically, the
nonsymmetric Whittaker function we introduced is
a quadratictype generating function of the levelone
Demazure characters for all (not only dominant)
weights. The new technique of Wspinors is used,
which is expected to influence classical real and
padic theory of Whittaker functions and find
applications in the theory of affine flag varieties.
I will also touch upon a surprising connection we
found to the PBWfiltration (an ongoing project
with Evgeny Feigin). The latter is closely related
to the Kostant qpartition function, though in a
way different from that for the Lusztig's qanalogs
of weight multiplicities and the BKfiltration. We
bumped into the Kostant qpartition function when
calculating the extremal qpowers for the socalled
Edagpolynomials, dual to the nonsymmetric
qHermite ones. This resulted in a new approach to
the PBWfiltrartion (E.Feigin, Fourier, Littelmann),
though only for extremal weights so far, which
will be discussed in the second half of the talk.
