Pre-canonical bases on affine Hecke algebras

2021/03/11 by Nicolás Libedinsky, Libedinsky, Nicolas, Leonardo Patimo +3 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Finite Group Theory Research

paper · pdf · doi:10.48550/arxiv.2103.06903

Abstract

For any affine Weyl group, we introduce the pre-canonical bases. They are a set of bases \Nⁱ\_{1≤ i ≤ m+1} (where m is the height of the highest root) of the spherical Hecke algebra that interpolates between the standard basis N¹ and the canonical basis N^m+1. The expansion of Nⁱ⁺¹ in terms of the Nⁱ is in many cases very simple and we conjecture that in type A it is positive.

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