Titlebook: Representation Theory, Number Theory, and Invariant Theory; In Honor of Roger Ho Jim Cogdell,Ju-Lee Kim,Chen-Bo Zhu Book 2017 Springer Inte

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Jim Cogdell,Ju-Lee Kim,Chen-Bo ZhuDetails recent advances in fields influenced by the work of Roger Howe.Based on talks given at the eponymous conference held at Yale University in 2015.Speakers include Roger Howe himself and other wo

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Estimates on Eisenstein Distributions for Reciprocals of ,-Adic ,-Functions: The Case of Irregular reciprocals of the Kubota-Leopoldt .-adic .-function. These distributions were shown there to be measures when . is regular. They fail to be measures when . is irregular; in this paper, we give quantitative estimates that describe their behavior more precisely.

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,Le Lemme Fondamental pour L’endoscopie Tordue: Le Cas où le Groupe Endoscopique Elliptique Non Ramiamifiée a pour groupe sous–jacent un tore. Cela entraîne que le lemme fondamental pour l’endoscopie tordue est désormais démontré, pour tous les éléments des algèbres de Hecke sphériques, en caractéristique nulle et en toute caractéristique résiduelle.

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,Euler-Poincaré Characteristic for the Oscillator Representation,element of the Grothendieck group of finite length representations of .′, and show that it is indeed more elementary than Hom(., .). We expect that computation of EP, together with vanishing results for higher Ext groups, will be a useful tool in computing the dual pair correspondence, and will help to elucidate the structure of Hom(., .).

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Derivatives and L-Functions for , ,,pend on invariant pairings between the derivatives of the representations of .. and ... We expect this way of computing .-functions will be applicable to other .-functions for .., such as the exterior square or symmetric square, as well as the local archimedean situation.

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Computations with Bernstein Projectors of SL(2),particular rely on the SL(2) discrete series character tables computed by Sally–Shalika in 1968. This new phenomenon for general rank has also been independently noticed in recent work of Bezrukavnikov, Kazhdan, and Varshavsky.