Yeah, I think potassium will positively effect on the microbial community especially under stress condition like salinity. 

Aimeric , very intelligently framed question . Having given a soil without any micronutrient constraint, application of  K  will induce an improvement in uptake efficiency of both N and P , and this  will  impose cascading effect on proliferation  of soil microbes by and large . however , certain K-solubilizers or silicate solubuilizers could further expand their number by metabolizing the additional K released from microbial action . Needless to say ,  effective microbes are biggest sink for nutrients N, P, and to a lesser extent  K  . Such solubilizers  will display much better resilience either under salinity or under any other abiotic stress,  as rightly opined by Alii.

Aimeric , let me add yet another response , every plant manufactures microbial diversity within its rhizosphere according to its metabolism. Take the one soil type  , grow different plant species , you will see huge difference  in microbial diversity . Likewise any change in soil pH  will surely induce change in both structural as well as functional change in microbial diversity .

@Aimeric, Soil microorganisms live mainly at expense of organic matter secreted  by plant roots and/or extracted from dead plant material. I think it must be a correlation between microbes and plant growth under different concentrations of Potassium.  Most of soils have enough K for microbial and plant growth. Experiments described  at the report of George Rehm "Soil cation ratios for crop production"  http://www.extension.umn.edu/agriculture/nutrient-management/soil-and-plant-sampling/soil-cation-ratios/, and other studies indicated that addition of extra K to soil will soon result in reduced plant yield, and, maybe, some decrease of microbial population consuming carbon and nitrogen from plants.

Thanks for your reply so far. Any publications/articles on the subject is welcome. I had a look, but I have been struggling to find articles on the subject.

To bring further my question to know exactly what we could expect on the effect of k input on soil microbial community (i.e. bacteria, archaea, fungi and functions) lets say we start with the same soil (e.g clay loam) and plant cover (grassland), and we had K (200 kg ha-1 ?) and N and P is not limiting at the beginning.

As you mention Alex, we are expecting after some time a reduction in the plant yield, and I would expect also a reduction in plant richness after some time (years to decades). I would not expect a rapid effect on microbial diversity but an indirect effect after couple of years due to the change of plant community. However, maybe we could expect a fairly rapid effect (within a year) on fungal community and especially mycorrhizal fungi which may increase in abundance or decrease (?) due to the change in plant community and root exudate. The rhizosphere may also respond quickly (matter of days, week, months or year?) due to the change of root exudate? I am intrigue by the timing that those change may occur. 

If we focus on specific microbial functions, such as the one related to the N cycle, are we expecting a decrease in N fixers abundance due to the increase in N available in soil if the plant are less efficient to uptake N because of K. On the other, are we expecting an increase of nitrification and denitrification due to an increase in N in soil (I guess it is purely dependent on the N form available even if an increase of N could happen).

We could also bring in the story the interaction of N and P as input, but it start to get complex...

Any point of views, if you think K is relevant or not for soil microorganisms, as important as N or P?

Intersting Aimeric.  saying K-fertilization will bring reduction in crop yiled , without considering other nutrients in tandem  , i strongly feel apprehensive about it .What i strongly feel about K-fertilization , that role of K is to be viewed to balance the excess application of N. The effect of balanced fertlization will only accrue when N,PK ratio is well amintained in the soil ,  without any micronutrient constraints.  This is the case across crops  and soil types, annual or perennial in nature. In illitic soils having richer K-reserve , we stress alot on the balance between N and K . Microbial niche within the rhizosphere will also respond that way .,  depending upon the composition of root exudates. Never forget,  every plant manufactures microbes  within its rhizosphere according to its metaboilc requirement .

What did you find in the end? What did K adittion do to microbial community?