CRM, 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.

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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