Context :

Aims : We analyse the effects of a first generation of fast rotating massive stars on the dynamical and chemical properties of globular clusters .

Methods : We use stellar models of fast rotating massive stars , losing mass through a slow mechanical equatorial winds to produce material rich in H-burning products .
We propose that stars with high Na and low O abundances ( hereafter anomalous stars ) are formed from matter made of slow winds of individual massive stars and of interstellar matter .
The proportion of slow wind and of interstellar material is fixed in order to reproduce the observed Li-Na anticorrelation in NGC 6752 .

Results : In the case that globular clusters , during their lifetime , did not lose any stars , we found that to reproduce the observed ratio of normal to anomalous stars , a flat initial mass function ( IMF ) is needed , with typically a slope x = 0.55 ( a Salpeter ’ s IMF has x = 1.35 ) .
In the case that globular clusters suffer from an evaporation of normal stars , the IMF slope can be steeper : to have x = 1.35 , about 96 % of the normal stars would be lost .
We make predictions for the distribution of stars as a function of their [ O/Na ] and obtain quite reasonable agreement with that one observed for NGC 6752 .
Predictions for the number fraction of stars with different values of helium , of the { } ^ { 12 } \kern - 0.6 ptC / { } ^ { 13 } \kern - 0.6 ptC and { } ^ { 16 } \kern - 0.6 ptO / { } ^ { 17 } \kern - 0.6 ptO ratios are discussed , as well as the expected relations between values of [ O/Na ] and those of helium , of [ C/N ] , of { } ^ { 12 } \kern - 0.6 ptC / { } ^ { 13 } \kern - 0.6 ptC and of { } ^ { 16 } \kern - 0.6 ptO / { } ^ { 17 } \kern - 0.6 ptO .
Future observations might test these predictions .
We also provide predictions for the present day mass of the clusters expressed in units of mass of the gas used to form stars , and for the way the present day mass is distributed between the first and second generation of stars and the stellar remnants .

Conclusions :