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Kazhdan–Lusztig basis and a geometric filtration of an affine Hecke algebra, II

Nanhua Xi (2011)

Journal of the European Mathematical Society

An affine Hecke algebras can be realized as an equivariant K -group of the corresponding Steinberg variety. This gives rise naturally to some two-sided ideals of the affine Hecke algebra by means of the closures of nilpotent orbits of the corresponding Lie algebra. In this paper we will show that the two-sided ideals are in fact the two-sided ideals of the affine Hecke algebra defined through two-sided cells of the corresponding affine Weyl group after the two-sided ideals are tensored by ℚ . This...

Knot theory with the Lorentz group

João Faria Martins (2005)

Fundamenta Mathematicae

We analyse perturbative expansions of the invariants defined from unitary representations of the Quantum Lorentz Group in two different ways, namely using the Kontsevich Integral and weight systems, and the R-matrix in the Quantum Lorentz Group defined by Buffenoir and Roche. The two formulations are proved to be equivalent; and they both yield ℂ[[h]]h-valued knot invariants related with the Melvin-Morton expansion of the Coloured Jones Polynomial.

Lemme fondamental et endoscopie, une approche géométrique

Jean-François Dat (2004/2005)

Séminaire Bourbaki

Le “principe de fonctorialité”, conjecturé par Langlands à la fin des années 60, est un moyen remarquablement synthétique d’unifier et exprimer certains liens profonds entre formes automorphes, arithmétique et géométrie algébrique. Son apparente simplicité contraste fortement avec la difficulté des techniques utilisées pour l’aborder. Parmi celles-ci, la stabilisation de la formule des traces d’Arthur–Selberg bute depuis 25 ans sur une conjecture d’analyse harmonique sur des groupes p -adiques :...

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