OP-SF WEB
Extract from OP-SF NET
CRM Workshop on Special Functions:
CRM, May 21-26, 1996
This is a report on the Atelier sur les méthodes
algébriques et q-fonctions spéciales (Workshop on
Algebraic Methods and q-special Functions), Centre de recherches
mathématiques, Université de Montréal, Montréal,
Québec, Canada, May 21-26, 1996.
Monday, May 20, was a national holiday in Canada (Victoria Day) and this
pushed the start of the workshop to Tuesday morning. Luc Vinet, co-organizer
with Pavel Winternitz and director of the Centre, opened the session at
9:00, welcomed the participants and dedicated the workshop to the memory of
Waleed Al-Salam, who passed away April 14 of this year (see
obituary). There were approximately seventeen invited
speakers who gave hour-long talks; there were about fourteen contributed
half-hour talks. David and Gregory Chudnovsky were invited but were unable
to attend and their time on the program was taken by other events. Sergei
Suslov was invited, could not attend, but Dick Askey delivered his lecture.
Dick also gave his own lecture (more details later). There was indeed a
heavy emphasis on q-special functions, both of one-variable
Askey-Wilson
type and of several-variable Macdonald type. The algebraic methods were
highly refined and sophisticated, mostly based on root systems and
associated mathematical objects such as double affine Hecke algebras. Here
is an alphabetical list of the invited speakers and the titles of their
lectures:
-
George Andrews: Plane partitions and MacMahon's partition analysis
- Richard Askey: An inequality of Vietoris and some related hypergeometric
sums
- Ivan Cherednik: Spherical difference Fourier transform
- Charles Dunkl: Intertwining operators and polynomials associated with the
symmetric group
- Pavel Etingof: Macdonald eigenvalue problem and representations of
quantum gl(n)
- Roberto Floreanini: Quantum algebras and generalized hypergeometric
functions
- Adriano Garsia: Polynomiality of the Macdonald q,t-Kostka
coefficients: a short proof
-
Mourad Ismail: Moment problems and orthogonal polynomials
- Tom Koornwinder: The A_1-tableau of Dunkl-Cherednik operators
- Boris Kupershmidt: The great powers of q-calculus
- Ian Macdonald: Symmetric and non-symmetric orthogonal polynomials
- David Masson: Contiguous relations, continued fractions and
orthogonality: a ten year journey up the Askey chart
- Willard Miller, Jr.: Tensor products of q-superalgebras and
q-series identities
- Masatoshi Noumi: Raising operators for Macdonald polynomials
- Eric Opdam: Spectral analysis of Hecke algebras
- Siddhartha Sahi: Recent results on Jack polynomials and Macdonald
polynomials
- Dennis Stanton: q-orthogonal polynomials as moments
- Sergei Suslov (talk delivered by R. Askey): Some basic hypergeometric
series and q-Bessel functions.
Contributed talks were given by N. Atakishiyev, R. Chouikha, P. Floris,
A. Grünbaum, K. Kadell, M. Kapilevich, J. LeTourneux, K. Mimachi,
A. Odzijewicz, V. Spiridonov, A. Strasburger, N. Takayama, F. van Diejen,
L. Vinet. Ian Macdonald started his lecture Tuesday morning and finished it on
Wednesday. Dick Askey gave an extra half-hour talk on Wednesday containing
an overview of Askey-Wilson polynomials. Tom Koornwinder used another one of
the hours originally scheduled for the Chudnovsky's to discuss René
Swarttouw's web site which gives access to a vast collection of formulas and
references for the polynomials contained in the Askey tableaux (q=1 and
general q). The URL is
http://www.can.nl/\symbol{126}renes/index.html;
see also the software announcement on
Askey-Wilson computer algebra mini-project. There were
approximately sixty participants; as well, some members of the Centre
dropped in on the lectures. The languages spoken at coffee and in the
hallways appeared to be English, Russian, French, Japanese, Dutch, Polish.
The weather was mostly delightful with a few evening showers. The
University is in a scenic location near Mont Royal; the Pavillon
André-Aisenstadt, which houses the Centre, is a beautifully
designed and equipped academic building, with a wonderful view of the
northwest of the city. Ian Macdonald gave the first lecture on Tuesday,
Adriano Garsia gave the last one on Saturday, thus bracketing an intense
period of leading-edge mathematics. It was generally agreed that the
workshop was excellent both in organization and inspiration to the
participants for future work. At the conclusion all applauded and thanked
the organizers for this exciting conference.
Charles Dunkl
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