Affine Hecke Algebras and Orthogonal Polynomials: The affine Hecke algebra

By Ian G. MacDonald. 2003

279 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/1fb008f0f9de9b5b5b6d6a9da6e8c03712dd6795

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Citations in the corpus

Refinements of the Littlewood-Richardson rule (2009, background): “In 1995 Macdonald [ 9 ] introduced a very general family of orthogonal polynomials called the nonsymmetric Macdonald polynomials E (Xn;q,t) which, although not symmetric functions, satisfy versions of most of the nice analytic and algebraic properties of the Jµ. Macdonald showed how to express Jµ as”
Whittaker functions and Demazure operators (2011, unknown): “See [25] for details.”
Generalized Jack polynomials and the representation theory of rational Cherednik algebras (2010, methodology): “We next calculate the norm of gS = e. fμ,T using a version of the argument proving (5.8.24) in [ 14 ].”
Buildings and Hecke algebras (2006, methodology): “To allow the reader to convert between our notation and that in [21], we provide the following instructions.”
From multiline queues to Macdonald polynomials via the exclusion process (2018, methodology): “Nonsymmetric Macdonald polynomials [8, 20] were introduced shortly after the introduction of Macdonald polynomials, and defined in terms of Cherednik operators; the symmetric Macdonald polynomials can be constructed from their nonsymmetric counterparts.”
Iwahori–Hecke algebras for p-adic loop groups (2014, background): “It is well-known ([29]) that Wo is itself an infinite Coxeter group which has simple reflection generators w1, .”
Double affine Hecke algebras and difference Fourier transforms (2001, methodology): “The previous papers [ M4 ,C4] and others devoted to the nonsymmetric polynomials were based on the pairing of type a). This conjugation is quite natural as |q |= 1, but creates certain problems in the real theory.”