Combinatorics, Symmetric Functions, and Hilbert Schemes

@inproceedings{Haiman2003CombinatoricsSF,
  title={Combinatorics, Symmetric Functions, and Hilbert Schemes},
  author={Mark D. Haiman},
  year={2003}
}
We survey the proof of a series of conjectures in combinatorics using new results on the geometry of Hilbert schemes. The combinatorial results include the positivity conjecture for Macdonald’s symmetric functions, and the “n!” and “(n + 1)n−1” conjectures relating Macdonald polynomials to the characters of doubly-graded Sn modules. To make the treatment self-contained, we include background material from combinatorics, symmetric function theory, representation theory and geometry. At the end… CONTINUE READING

From This Paper

Topics from this paper.

References

Publications referenced by this paper.
Showing 1-10 of 59 references

Techniques de construction et théorèmes d’existence en géométrie algébrique

Alexander Grothendieck
IV. Les schémas de Hilbert (Exp • 1995
View 11 Excerpts
Highly Influenced

On certain graded Sn-modules and the q-Kostka polynomials

A. M. Garsia, C. Procesi
Adv. Math. 94 • 1992
View 20 Excerpts
Highly Influenced

A q-analogue of the Lagrange inversion formula

Adriano M. Garsia
Houston J. Math • 1981
View 20 Excerpts
Highly Influenced

A noncommutative generalization and q-analog of the Lagrange inversion formula

Ira Gessel
Trans. Amer. Math. Soc • 1980
View 8 Excerpts
Highly Influenced

The McKay correspondence as an equivalence of derived categories

Tom Bridgeland, Alastair King, Miles Reid
J. Amer. Math. Soc • 2001
View 11 Excerpts
Highly Influenced

McKay correspondence

M. Reid
Electronic preprint, arXiv:alg-geom/9702016 • 1997
View 10 Excerpts
Highly Influenced

Similar Papers

Loading similar papers…