Nakajima varieties and repetitive algebras

We realize certain graded Nakajima varieties of finite Dynkin type as orbit closures of repetitive algebras of Dynkin quivers. As an application, we obtain that the perverse sheaves introduced by Nakajima for describing irreducible characters of quantum loop algebras are isomorphic to the intersection cohomology sheaves of these orbit closures.Comment: 26 pages, v2 : Minor corrections. Final version to appear in PRIMS (Publications of the Research Institute for Mathematical Sciences, Kyoto

Cluster algebras via cluster categories with infinite-dimensional morphism spaces

We apply our previous work on cluster characters for Hom-infinite cluster categories to the theory of cluster algebras. We give a new proof of Conjectures 5.4, 6.13, 7.2, 7.10 and 7.12 of Fomin and Zelevinsky's Cluster algebras IV for skew-symmetric cluster algebras. We also construct an explicit bijection sending certain objects of the cluster category to the decorated representations of Derksen, Weyman and Zelevinsky, and show that it is compatible with mutations in both settings. Using this map, we give a categorical interpretation of the E-invariant and show that an arbitrary decorated representation with vanishing E-invariant is characterized by its g-vector. Finally, we obtain a substitution formula for cluster characters of not necessarily rigid objects.Comment: 32 pages, added referenc

Towards an Automatic Dictation System for Translators: the TransTalk Project

Professional translators often dictate their translations orally and have them typed afterwards. The TransTalk project aims at automating the second part of this process. Its originality as a dictation system lies in the fact that both the acoustic signal produced by the translator and the source text under translation are made available to the system. Probable translations of the source text can be predicted and these predictions used to help the speech recognition system in its lexical choices. We present the results of the first prototype, which show a marked improvement in the performance of the speech recognition task when translation predictions are taken into account.Comment: Published in proceedings of the International Conference on Spoken Language Processing (ICSLP) 94. 4 pages, uuencoded compressed latex source with 4 postscript figure