Resumen de Representation theory and the cohomology of arithmetic groups

B. Speh

• Let G be a semisimple Lie group with finitely many connected components and Lie algebra g, K a maximal compact subgroup of G, and X = G/K a symmetric space. A torsion free discrete subgroup  of G and a finite dimensional real or complex linear representation (¥ñ,E) of G define a locally symmetric space X = \G/K with a local system E.. Then H.(,E) = H.(\X, E.) is isomorphic to H.(g,K,C¡Ä(\G) . E). If  is an arithmetic group, thenH.(g,K,C¡Ä(\G).E) is isomorphic to the (g,K)-cohomology with coefficients inA(\G).E whereA(\G) is the space of automorphic forms. Using representation theory and the theory of automorphic forms a large amount of information about H.(,E) can be deduced.