============================================================================= 6th Conference on 6eme Colloque Formal Power Series S\'eries Formelles and Algebraic Combinatorics et Combinatoire Alg\'ebrique FPSAC '94 SFCA '94 DIMACS DIMACS May 23-27, 1994 23-27 mai 1994 ============================================================================= SELECTED READINGS SELECTIONS BIBLIOGRAPHIQUES recommended by the recommend\'ees par les invited speakers conf\'erenciers invit\'es Phil HANLON, ``Combinatorial problems connected to the homology of Lie algebras'' Basics about Lie algebras and Lie algebra homology: 1) J.E.Humphreys, Introduction to Lie Algebras and Representation Theory, Springer Graduate Texts in Mathematics #9. 2) J.L.Koszul, "Homologie et cohomologie des alg\`ebres de Lie", Bull. Math. Soc. France, 78 (1950), 65-127. (the seminal work on the subject) 3) Most standard texts in homological algebra have some introduction to Lie algebra homology, eg., Rotman, Hilton & Stammbach, Cartan & Eilenberg. More directly relevant to this talk: 4) B.Kostant, "Lie algebra cohomology and the generalized Borel-Weil Theorem", Ann. of Math. 74 (1961), 329-387. (very technical but a dynamite paper) 5) H.Garland and J.Lepowsky, "Lie algebra homology and the Macdonald-Kac formulas", Inv. Math. 34 (1976), 37-76. (same comment as 4)). 6) J.Stembridge, "First layer formulas for characters of SL(n,C), Trans.AMS 299, #1 (1987), 319-350. 7) I.G.Macdonald, "Some conjectures for root systems", SIAM J. Math. Anal. 13 (1982), 988-1007. 8) J.L.Loday and D.Quillen, "Cyclic homology and the Lie algebra homology of matrices", Comm. Math. Helv. 59 (1984), 565-591. (see also the new book, "Cyclic Homology", by J.L.Loday, Springer Grundlehren der mathematischen Wissenschaften #301). 9) R.P.Stanley, "The stable behavior of some characters of SL(n,C)", J. Linear and Multilinear Alg. 16 (1984), 3-27. 10) P.Hanlon, "Cyclic homology and the Macdonald conjectures", Inv. Math., 86 (1986), 131-159. 11) P.Hanlon, "Some conjectures and results concerning the homology of nilpotent Lie algebras", Adv. Math. Vol.84, #1 (1990), 91-134.