Symmetric functions and Macdonald polynomials
SFM
8 January 2001 to 6 July 2001
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Programme theme
The importance of symmetric functions and the representation theory of Hecke algebras and the symmetric groups derives in part from their applicability in a wide range of scientific and mathematical disciplines. Within the theory of symmetric functions, this programme will focus on a particular topic, the Macdonald polynomials, which have especially wide-ranging mathematical interconnections. The goal of the program will be to unify the diverse approaches to the study of these polynomials.
n the 1980's, I.G.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 Conjectures in a way that allows for a significant interpretation of the Macdonald polynomials and settles some of the outstanding conjectures that have resulted from this work.
Links with other areas such as algebraic geometery, Lie algebras, non-commutative algebra, mathematical physics and mathematical statistics will be emphasised. Workshops will be arranged in order to foster existing and potential applications in these and other subjects.
Click here to download the programme's final scientific report
Preprints
| Title | Year | Programme |
|---|---|---|
Combinatorial models for Weyl charactersAuthors: John Stembridge |
2000 | SFM |
A Weighted Enumeration of Maximal Chains in the Bruhat OrderAuthors: John Stembridge |
2000 | SFM |
Solutions of the periodic Toda lattice via the projection procedure and by the algebra-geometric methodAuthors: Mikhail Olshanetsky |
2000 | SFM |
Classification of graded Hecke algebras for complex reflection groupsAuthors: A Shepler, A Ram |
2000 | SFM |
About division by 1Authors: A Lascoux |
2000 | SFM |
The Newton interpolation formula, with more variablesAuthors: A Lascoux |
2000 | SFM |
The Laurent phenomenonAuthors: Andrei Zelevinsky, Sergey Fomin |
2000 | SFM |
Elliptic Selberg IntegralsAuthors: VP Spiridonov, JF Van Diejen |
2000 | SFM |
Noncommutative symmetric functions VI: Free quasi-symmetric functions and related algebrasAuthors: Gerard Duchamp, Florent Hivert, Jean-Yves Thibon |
2000 | SFM |
Vanishing theorems and character formulas for the Hilbert scheme of points in the planeAuthors: Mark Haiman |
2000 | SFM |
Representations of graded Hecke algebrasAuthors: A Ram, C Kriloff |
2000 | SFM |
Projective Schur functions as a bispherical functions on certain homogenous superspacesAuthors: Alexander Sergeev |
2000 | SFM |
Vertex operators and the class algebras of symmetric groupsAuthors: Jean-Yves Thibon, A Lascoux |
2000 | SFM |
Dunkl operators for complex reflection groupsAuthors: Eric Opdam, Charles Dunkl |
2000 | SFM |
Affine braids, Markov traces and the category 0Authors: A Ram, R Orellana |
2000 | SFM |
Superanalogs of the Calogero operators and Jack polynomialsAuthors: Alexander Sergeev |
2000 | SFM |
The $_q-$deformed algebra U'$_q$(so$_n$) related to Macdonald Symmetric polynomialsAuthors: Anatoli Klimyk |
2000 | SFM |
Noncommutative symmetric functions and quasi-symmetric functions with two and more parametersAuthors: A Lascoux, Jean-Yves Thibon, Florent Hivert |
2000 | SFM |
On the property M conjecture for the Heisenberg Lie algebraAuthors: M Wachs, Phil Hanlon |
2000 | SFM |
Geometrically constructed bases for homology of partition lattices of types A, B and DAuthors: A Bjorner, M Wachs |
2000 | SFM |
Modular hypergeometric residue sums of elliptic Selberg integralsAuthors: VP Spiridonov, JF Van Diejen |
2000 | SFM |
q-rook monoid algebras, Hecke algebras, and Schur-Weyl dualityAuthors: A Ram, T Halverson |
2000 | SFM |
Symmetric functions in noncommutative variablesAuthors: Mercedes Rosas, Bruce Sagan |
2000 | SFM |
Workshops
Euro workshop: conjectures, recent results and open problems related to the Macdonald polynomials
8 January 2001 to 12 January 2001
Euro conference: applications of the Macdonald polynomials
16 April 2001 to 21 April 2001
The heritage of I Schur's 1901 dissertation
2 June 2001 to 5 June 2001
A NATO ASI - symmetric functions 2001: surveys of developments and perspectives
25 June 2001 to 6 July 2001
Organisers
- Phil Hanlon University of Michigan
- Ian Macdonald
- Alun Morris University of New South Wales
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