Homological algebra/Topology
Two functions on Sp(g,R)
[Deux fonctions sur Sp(g,R)]

Présenté par : Michèle Vergne

Gilmer, Patrick M.1
1 Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803, USA
Comptes Rendus. Mathématique, Tome 353 (2015) no. 6, pp. 477-481.

Nous considérons deux fonctions sur Sp(g,R) à valeurs dans le groupe cyclique d'ordre quatre {±1,±i}. L'une a été définie par Lion et Vergne. L'autre est −i élevé à la puissance donnée par une fonction à valeurs entières définie par Masbaum et l'auteur (initialement sur le groupe modulaire d'une surface). Nous montrons que ces deux fonctions coïncident sur Sp(g,Z). Nous conjecturons qu'elles coïncident sur Sp(g,R).

We consider two functions on Sp(g,R) with values in the cyclic group of order four {±1,±i}. One was defined by Lion and Vergne. The other is −i raised to the power given by an integer valued function defined by Masbaum and the author (initially on the mapping class group of a surface). We identify these functions when restricted to Sp(g,Z). We conjecture the identity of these functions on Sp(g,R).

Reçu le :
Accepté le :
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DOI : 10.1016/j.crma.2015.03.006
Gilmer, Patrick M. 1

1 Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803, USA 
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Gilmer, Patrick M. Two functions on $ \mathrm{Sp}(g,\mathbb{R})$. Comptes Rendus. Mathématique, Tome 353 (2015) no. 6, pp. 477-481. doi : 10.1016/j.crma.2015.03.006. http://www.numdam.org/articles/10.1016/j.crma.2015.03.006/

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