mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

, the Macdonald identities are some infinite product identities associated to

affine root system In mathematics, an affine root system is a root system of affine-linear functions on a Euclidean space. They are used in the classification of affine Lie algebras and superalgebras, and semisimple ''p''-adic algebraic groups, and correspond to f ...

s, introduced by . They include as special cases the Jacobi triple product identity, Watson's

quintuple product identity In mathematics the Watson quintuple product identity is an infinite product identity introduced by and rediscovered by and . It is analogous to the Jacobi triple product identity, and is the Macdonald identity for a certain non-reduced affine roo ...

, several identities found by , and a 10-fold product identity found by . and pointed out that the Macdonald identities are the analogs of the Weyl denominator formula for affine Kac–Moody algebras and superalgebras.

References

* * * * * *{{Citation , last1=Winquist , first1=Lasse , title=An elementary proof of p(11m+6) ≡ 0 mod 11 , mr=0236136 , year=1969 , journal=Journal of Combinatorial Theory , volume=6 , pages=56–59 , doi=10.1016/s0021-9800(69)80105-5, doi-access=free Lie algebras Mathematical identities Infinite products