For any affine Weyl group, we introduce the pre-canonical bases. They are a set of bases {N-i}1 <= i <= m+1 (where m is the height of the highest root) of the spherical Hecke algebra that interpolates between the standard basis N-1 and the canonical basis Nm+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.
Pre-canonical bases on affine Hecke algebras
Patimo L.;
2022-01-01
Abstract
For any affine Weyl group, we introduce the pre-canonical bases. They are a set of bases {N-i}1 <= i <= m+1 (where m is the height of the highest root) of the spherical Hecke algebra that interpolates between the standard basis N-1 and the canonical basis Nm+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.File in questo prodotto:
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