Galleries, Hall-Littlewood polynomials, and structure constants of the spherical Hecke algebra
By Christoph Schwer. 2005
63 citations recorded by the source corpus.
We provide a combinatorial description of the coefficients appearing in the expansion of Hall-Littlewood polynomials in terms of monomial symmetric functions. We also give a Littlewood-Richardson rule for Hall-Littlewood polynomials. For proving this we use galleries to calculate Satake coefficients and structure constants of spherical Hecke algebras with arbitrary parameters.
Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/d61605018b5d7b49bd2707aeb6842c067498a0fd
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Algebra and Number Theory
In Discrete Mathematics and Combinatorics
In Geometry and Topology
Citations in the corpus
- From multiline queues to Macdonald polynomials via the exclusion process (2018, unknown): “Building on work of Schwer [Sch06], Ram and Yip [RY11] gave general-type formulas for both the Macdonald polynomials Pλ(x; q, t) and the nonsymmetric Macdonald polynomials; however, their type A formulas have many terms.”
- Buildings and Hecke algebras (2006, background): “The elements of C are called chambers, and we write c ∼i d to mean that the chambers c and d are i-adjacent.”
- A combinatorial formula for Macdonald polynomials (2008, unknown): “Schwer [16], the paper [15] developed a combinatorics for working in the affine Hecke algebra, the alcove walk model.”