A Proof of the $G_2 $ Case of Macdonald’s Root System-Dyson Conjecture

DOI10.1137/0518065zbMath0643.05004OpenAlexW2023856866WikidataQ123219663 ScholiaQ123219663MaRDI QIDQ3784074

Doron Zeilberger

Publication date: 1987

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/0518065

zbMATH Keywords

Selberg's integral\(G_ 2\) caseconstant term of the Laurent polynomialLaurent HabsiegerMacdonald's Root System-Dyson conjecture

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Simple, semisimple, reductive (super)algebras (17B20) Classical hypergeometric functions, ({}_2F_1) (33C05)

Related Items (12)

Macdonald’s constant term conjectures for exceptional root systems ⋮ Character sum identities in analogy with special functions identities ⋮ Unnamed Item ⋮ Problems on the Z-statistic ⋮ Twisted strong Macdonald theorems and adjoint orbits ⋮ The importance of the Selberg integral ⋮ A one-line proof of the Habsieger-Zeilberger \(G_ 2\) constant term identity ⋮ A proof of the two parameter \(q\)-cases of the Macdonald-Morris constant term root system conjecture for \(S(F_ 4)\) and \(S(F_ 4)^ \vee\) via Zeilberger's method ⋮ A generalization of Selberg’s beta integral ⋮ Logarithmic and Complex Constant Term Identities ⋮ On the \(q\)-Dyson orthogonality problem ⋮ MultInt, a MAPLE package for multiple integration by the WZ method

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