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If t=1 the Macdonald polynomials become the sums over W orbits, which are the monomial symmetric functions when the root system has type A. If we put t = q α and let q tend to 1 the Macdonald polynomials become Jack polynomials when the root system is of type A , and Heckman–Opdam polynomials for more general root systems.
In mathematics, the Macdonald identities are some infinite product identities associated to affine root systems, introduced by Ian Macdonald . They include as special cases the Jacobi triple product identity , Watson's quintuple product identity , several identities found by Dyson (1972) , and a 10-fold product identity found by Winquist (1969) .
This is a list of special function eponyms in mathematics, ... Ian G. Macdonald: Macdonald polynomial, Macdonald–Kostka polynomial, Macdonald spherical function.
A ring of symmetric functions can be defined over any commutative ring R, and will be denoted Λ R; the basic case is for R = Z. The ring Λ R is in fact a graded R-algebra. There are two main constructions for it; the first one given below can be found in (Stanley, 1999), and the second is essentially the one given in (Macdonald, 1979).
A Missouri woman who admitted to killing her husband because she couldn’t afford to divorce him has been sentenced to 10 years in prison. On Monday, Jan. 27, Melanie Biggins, 42, pleaded guilty ...
The affine root system of type G 2.. 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 families of Macdonald polynomials.
Today's NYT Connections puzzle for Wednesday, February 19, 2025The New York Times
In healthy brains, tau binds to—and stabilizes—microtubules, which are hollow structures that play important roles in the structure, function, and development of the brain, according to the ...