Wed, February 17, 2021
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2:00pm [2:00pm] Sagar Kalane, IISER Pune
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Date and Time: Wednesday, 17th February 2021 at 2 PM Google Meet Link: https://meet.google.com/zif-jpge-ybc?hs=122&authuser=1 Speaker: Sagar Kalane, IISER Pune Title: Classification of pairs of quaternionic and complex hyperbolic isometries Abstract: Consider the Lie groups G=SU(n, 1) and Sp(n, 1) that act as isometries of the complex and the quaternionic hyperbolic spaces respectively. In this talk, we will classify pairs of semisimple elements in Sp(n, 1) and SU(n, 1) up to conjugacy. This gives local parametrization of the representations ρ in deformation space Hom(F2, G)/G such that both ρ(x) and ρ(y) are semisimple elements in G, where F2 = , G = Sp(n, 1) or SU(n, 1). Also, we shall classify conjugation orbits of non-singular pairs of loxodromic elements in SU(n,1). This is a survey of joint work with Krishnendu Gongopadhyay
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