BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Sebastian Bischof (Uni Giesen) DTSTART:20220204T033000Z DTEND:20220204T043000Z DTSTAMP:20260423T021438Z UID:SiN/35 DESCRIPTION:Title: (Tw in) Buildings and groups\nby Sebastian Bischof (Uni Giesen) as part of Symmetry in Newcastle\n\nLecture held in SR118\, Callaghan Campus.\n\nAbs tract\nBuildings have been introduced by Tits in order to study semi-simpl e algebraic groups from a geometrical point of view. One of the most impor tant results in the theory of buildings is the classification of thick irr educible spherical buildings of rank at least 3. In particular\, any such building comes from an RGD-system. The decisive tool in this classificatio n is the Extension theorem for spherical buildings\, i.e. a local isometry extends to the whole building.\nTwin buildings were introduced by Ronan a nd Tits in the late 1980s. Their definition was motivated by the theory of Kac-Moody groups over fields. Each such group acts naturally on a pair of buildings and the action preserves an opposition relation between the cha mbers of the two buildings. This opposition relation shares many important properties with the opposition relation on the chambers of a spherical bu ilding. Thus\, twin buildings appear to be natural generalizations of sphe rical buildings with infinite Weyl group. Since the notion of RGD-systems exists not only in the spherical case\, one can ask whether any twin build ing (satisfying some further conditions) comes from an RGD-system. In 1992 Tits proves several results that are inspired by his strategy in the sphe rical case and he discusses several obstacles for obtaining a similar Exte nsion theorem for twin buildings. In this talk I will speak about the hist ory and developments of the Extension theorem for twin buildings.\n LOCATION:https://researchseminars.org/talk/SiN/35/ END:VEVENT END:VCALENDAR