zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
La q-conjecture de Macdonald-Morris pour G 2 . (The q-conjecture of Macdonald-Morris for G 2 ). (French) Zbl 0598.05006

The author proves the Macdonald-Morris conjecture for the value of the coefficient of e 0 in

' ( i=1 a (1-e α q i-1 )(1-e -α q i )), '' ( i=1 b (1-e β q i-1 )(1-e -β q i ))

where ' is a product over the positive long roots of G 2 and '' is a product over the positive short roots of G 2 . The proof derives this identity from the evaluation of a ”q-Selberg multidimensional beta integral”, an evaluation found independently by L. Habsieger [ibid. 302, 615-617 (1986)] and K. Kadell. The derivation of the G 2 result from the q-Selberg evaluation was independently realized in the same week by D. Zeilberger.

Reviewer: D.M.Bressoud

MSC:
05A15Exact enumeration problems, generating functions
17B20Simple, semisimple, reductive Lie (super)algebras
33B15Gamma, beta and polygamma functions