Some Conjectures for Root Systems

1982/11/01 by I. G. Macdonald · 275 citations
Mathematics · #Random Matrices and Applications #Advanced Combinatorial Mathematics #Advanced Algebra and Geometry #Mathematics #Conjecture #Root (linguistics) #Pure mathematics #Root system #Combinatorics

paper · doi:10.1137/0513070

published in SIAM Journal on Mathematical Analysis 13(6), 988-1007 (Society for Industrial and Applied Mathematics)

openalex publication_date 1982/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/08

Abstract

We present a collection of conjectures relating to root systems (or, equivalently, to Lie groups) together with the evidence we possess in support of them. They may be regarded as generalizations of Dyson’s conjecture [J. Math. Phys. 3 (1962), pp. 140–156] and Mehta’s conjecture [Random Matrices, Academic Press, New York, 1967].

Citations

• Affine root systems and Dedekind's?-function
• A duality for symmetric spaces with applications to group representations
• Spherical Functions on a Semisimple Lie Group, I

Cited by

• Double Affine Hecke Algebras and Macdonald's Conjectures
• Dyson conjecture [wikipedia]
• Selberg integral [wikipedia]