Geometric cycles in compact Riemannian locally symmetric spaces of type IV and automorphic representations of complex simple Lie groups

2019/12/09 by Paul, Pampa · 1 citation
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1912.04330

Abstract

Let G be a connected complex simple Lie group with maximal compact subgroup U. Let g be the Lie algebra of G, and X = G/U be the associated Riemannian globally symmetric space of type IV. We have constructed three types of arithmetic uniform lattices in G, say of type 1, type 2, and type 3 respectively. If g is not equal to b_n, n&gt;0, then for each 0<i>4), c_n (n &gt; 5), or f₄. To prove these, we have simplified Kac's description of finite order automorphisms of g with respect to a Chevalley basis of g. Also we have determined some orientation preserving group action on some subsymmetric spaces of X.</i>

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