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math.RT2026
The asymptotic Plancherel formula and Lusztig's asymptotic algebra for
Nathan Chapelier-Laget, Jérémie Guilhot, Eloise Little +1
The aim of this paper is to give a new explicit construction of Lusztig's asymptotic algebra in affine type . To do so, we construct a balanced system of cell modules,…
math.RT2026
Kazhdan-Lusztig bases of parabolic Hecke algebras and applications to Schur-Weyl duality
Jeremie Guilhot, Loic Poulain d'Andecy
With an eye to applications to type A and Schur-Weyl duality, we study Kazhdan-Lusztig bases for a general parabolic Hecke algebra. Parabolic Hecke algebras are idempotent subalgeb…
math.RT2024
On -folded alcove paths and combinatorial representations of affine Hecke algebras
Jérémie Guilhot, Eloise Little, James Parkinson
We introduce the combinatorial model of -folded alcove paths in an affine Weyl group and construct representations of affine Hecke algebras using this model. We study boundednes…