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I am learning representation theory of Lie groups & Lie algebras from the book by Brian Hall. Unfortunately, this does not discuss infinite dimensional representations. Which books should I study for this when I complete my study of Brian Hall's book?

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The following lecture notes of James E. Humphreys on "Representations of Semisimple Lie Algebras in the BGG Category O" might be interesting for you, also including infinite-dimensional representations of finite-dimensional Lie algebras, and much more: http://www.math.umass.edu/~jeh/bgg/main.pdf.

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You could try Kac, Victor G. Infinite-dimensional Lie algebras. Third edition. Cambridge University Press, Cambridge, 1990.

Here is a paper by Bernstein and Gelfand that seems pretty influential:

Bernstein, J. N.; Gelʹfand, S. I. Tensor products of finite- and infinite-dimensional representations of semisimple Lie algebras. Compositio Math. 41 (1980), no. 2, 245–285.

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    $\begingroup$ Thanks! Just one question. Does this book deal with infinite dimensional representations of finite dimensional Lie algebras as well or focuses entirely on infinite dimensional Lie algebras and their representations? $\endgroup$
    – user90041
    Oct 13, 2013 at 15:27

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