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Host: Isaac Newton Institute for Mathematical Sciences
Homepage: http://www.newton.cam.ac.uk/programs/sfmw01.html
Organizers: Professor P Hanlon, Professor IG Macdonald, Professor AO Morris
Description:
In the 1980s, IG Macdonald formulated a series of conjectures which predicted the constant terms of
expressions that involve an important new class of symmetric functions called the Macdonald polynomials. Since their
introduction, these conjectures and polynomials have been a central topic of study in Algebraic Combinatorics. Of particular note
has been the variety of approaches used in efforts to solve the conjectures or to find an algebraic or geometric interpretation for the
Macdonald polynomials themselves. Different approaches involve double affine Hecke algebras, homology of nilpotent Lie
algebras, generalized traces of Lie algebra representations and diagonal actions of the symmetric group on polynomial rings in two
sets of variables. In this programme we will attempt to unify these different approaches to the Macdonald polynomials and some of
the outstanding conjectures that have resulted from this work. Links with other areas such as algebraic geometry, Lie algebras,
non-commutative algebra, mathematical physics and mathematical statistics will be emphasised.
Date received: October 11, 2000
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