Journal of Algebraic Combinatorics

, Volume 3, Issue 1, pp 17–76

Conjectures on the Quotient Ring by Diagonal Invariants

  • Mark D. Haiman

DOI: 10.1023/A:1022450120589

Cite this article as:
Haiman, M.D. Journal of Algebraic Combinatorics (1994) 3: 17. doi:10.1023/A:1022450120589


We formulate a series of conjectures (and a few theorems) on the quotient of the polynomial ring \(\mathbb{Q}[x_1 , \ldots ,x_n ,y_1 , \ldots ,y_n ]\) in two sets of variables by the ideal generated by all Sn invariant polynomials without constant term. The theory of the corresponding ring in a single set of variables X = {x1, ..., xn} is classical. Introducing the second set of variables leads to a ring about which little is yet understood, but for which there is strong evidence of deep connections with many fundamental results of enumerative combinatorics, as well as with algebraic geometry and Lie theory.

diagonal harmonicsinvariantCoxeter group

Copyright information

© Kluwer Academic Publishers 1994

Authors and Affiliations

  • Mark D. Haiman
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaSan Diego