First of all, I am coming from Java background so please forgive me for my mistakes:

This is my class

 class ParameterHandler<T>
 {

        public static Dictionary<string, Converter<T>> parameters =
               new Dictionary<string, Converter<T>>();

        public static void addParameter(string parameterName, Converter<T> converter){
            parameters.Add(parameterName, converter);
        }

        static T getValue(string parameterName, string stringValue){
            return parameters[parameterName].getValue(stringValue);
        }
 }

and this is my Converter interface

interface Converter <T>
{
        T getValue(string stringValue);
}

I wonder if I can use the parameterhandler without having to declare T as a generic type for it

I just need to do something like

ParameterHandler.addParameter("some", Some Implementation for Converter)

and to put you in the whole picture, this is one of my implementation for the Converter

class IntConverter : Converter<int>
{
        int getValue(string stringValue)
        {
            return int.Parse(stringValue);
        }
}

You must define an interface that is base for all converters:

 interface Converter
 {
 }
 interface Converter<T> : Converter
 {
     T getValue(string stringValue);
 }

Then:

class ParameterHandler
{
    public static Dictionary<string, Converter> parameters =
           new Dictionary<string, Converter>();

    public static void addParameter<T>(string parameterName, Converter<T> converter){
        parameters.Add(parameterName, converter);
    }

    static T getValue<T>(string parameterName, string stringValue){
        if(!parameters[parameterName] is Convereter<T>)
             throw new Exception("Invalid Type");

        return ((Convereter<T>)parameters[parameterName]).getValue(stringValue);
    }
}

Note that, in your initial model, you have a different dictionary for each type T, Converter<int>.parameters and Converter<double>.parameters are not the same.

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