Plenty of books about on GLMs for exponential families, but any good books or papers which study the Dirichlet distribution in particular?
The book by Ludwig Fahrmeir Gerhard Tutz: "Multivariate Statistical Modelling Based on Generalized Linear Models (Second Edition)" contain some references, but it seems to be mostly to use of the dirichlet distribution as a prior distribution in multinomial logistic models. There are many papers on Dirichlet regression, see https://www.researchgate.net/profile/Rafiq_Hijazi/publication/228576713_Modelling_compositional_data_using_Dirichlet_regression_models/links/02e7e52e9cab9696f5000000.pdf or https://www.researchgate.net/profile/Rafiq_Hijazi/publication/265165887_Residuals_and_Diagnostics_in_Dirichlet_Regression/links/54054b8c0cf2c48563b13827.pdf . But are these models GLM's? see for instance Why Beta/Dirichlet Regression are not considered Generalized Linear Models?