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Affine root systems and Dedekind’s $\eta$-function. (English) Zbl 0244.17005
Reviewer: H. Reitberger

##### MSC:
 17B20 Simple, semisimple, reductive Lie (super)algebras 11F22 Relationship of automorphic forms to Lie algebras, etc.
##### References:
 [1] Bourbaki, N.: Groupes et algèbres de Lie, Chapitres 4, 5, et 6. Paris: Hermann 1969. [2] Bruhat, F., Tits, J.: Groupes réductifs sur un corps local. Publ. Math. I.H.E.S., 41 (to appear). [3] Freudenthal, H., Vries, H. de: Linear Lie groups. New York: Academic Press 1969. [4] Hardy, G. H., Wright, E. M.: Introduction to the theory of numbers (4th edition). Oxford: Oxford University Press 1959. [5] Kostant, B.: The principal three-dimensional subgroup and the Betti numbers of a complex simple Lie group. Amer. J. Math.81, 973-1032 (1959). · Zbl 0099.25603 · doi:10.2307/2372999 [6] Macdonald, I. G.: The Poincaré series of a Coxeter group (to appear). [7] Winquist, L.: Elementary proof ofp(11m+6)?0 (mod 11). J. Comb. Theory6, 56-59 (1969). · Zbl 0241.05006 · doi:10.1016/S0021-9800(69)80105-5 [8] Moody, R. V.: A new class of Lie algebras. J. Alg.10, 211-230 (1968). · Zbl 0191.03005 · doi:10.1016/0021-8693(68)90096-3 [9] ?: Euclidean Lie algebras. Can. J. Math.21, 1432-1454 (1969). · doi:10.4153/CJM-1969-158-2