Symmetric Functions 2001: Surveys of Developments and Perspectives: Surveys of Developments and Perspectives : [proceedings of the NATO Advanced Study Institute on ... Cambridge, U.K., 25 June - 6 July 2001]Sergey Fomin This volume contains the proceedings of the NATO Advanced Study Institute "Symmetric Functions 2001: Surveys of Developments and Per- spectives", held at the Isaac Newton Institute for Mathematical Sciences in Cambridge, UK, during the two weeks 25 June - 6 July 2001. The objective of the ASI was to survey recent developments and outline research perspectives in various fields, for which the fundamental questions can be stated in the language of symmetric functions (along the way emphasizing interdisciplinary connections). The instructional goals of the event determined its format: the ASI consisted of about a dozen mini-courses. Seven of them served as a basis for the papers comprising the current volume. The ASI lecturers were: Persi Diaconis, William Fulton, Mark Haiman, Phil Hanlon, Alexander Klyachko, Bernard Leclerc, Ian G. Macdonald, Masatoshi Noumi, Andrei Okounkov, Grigori Olshanski, Eric Opdam, Ana- toly Vershik, and Andrei Zelevinsky. The organizing committee consisted of Phil Hanlon, Ian Macdonald, Andrei 0 kounkov, G rigori 0 lshanski (co-director), and myself ( co-director). The original ASI co-director Sergei Kerov, who was instrumental in determining the format and scope of the event, selection of speakers, and drafting the initial grant proposal, died in July 2000. Kerov's mathemat- ical ideas strongly influenced the field, and were presented at length in a number of ASI lectures. A special afternoon session on Monday, July 2, was dedicated to his memory. |
Contents
NOTES ON MACDONALD POLYNOMIALS AND THE GEOMETRY OF HILBERT SCHEMES | 1 |
THE LAPLACIAN METHOD | 65 |
KEROVS CENTRAL LIMIT THEOREM FOR THE PLANCHEREL MEASURE ON YOUNG DIAGRAMS | 93 |
SYMMETRIC FUNCTIONS AND THE FOCK SPACE | 153 |
AN INTRODUCTION TO BIRATIONAL WEYL GROUP ACTIONS | 179 |
SYMMETRIC FUNCTIONS AND RANDOM PARTITIONS | 223 |
FROM LITTLEWOODRICHARDSON COEFFICIENTS TO CLUSTER ALGEBRAS IN THREE LECTURES | 253 |
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Symmetric Functions 2001: Surveys of Developments and Perspectives Sergey Fomin Limited preview - 2002 |
Symmetric Functions 2001: Surveys of Developments and Perspectives ... Sergey Fomin Limited preview - 2012 |
Common terms and phrases
action affine algebraic complex asymptotics automorphisms basis bijection birational Sn-action canonical bases Cartan matrix central limit theorem cluster algebra coefficients cohomology combinatorial compute conjecture coordinate ring corresponding decomposition defined definition denote diagonal eigenvalues elements equal example fiber finite Fock space Fomin Gaussian geometric given Gorenstein graded Hence Hilbert scheme homogeneous homology ideal implies integral inverse irreducible isomorphism Jacobi-Trudi formula kernel Kerov Laplacian lectures Lemma Lie algebra linear Lusztig Macdonald polynomials Math monomials morphism multiplicity notation Note obtained parameters partition permutation Plancherel measure Proposition prove random matrices random variables rational functions reduced regular functions relations representation result Schur function Section sequence sheaf subset symmetric functions symmetric group Theorem 6.1 total positivity unique University vanish vector space W-action Weyl group Young diagrams Zelevinsky